Gr 10 Math Ch 4 SUM: Trigonometry

What is the length of the hypotenuse in a 30°-60°-90° triangle?

√3

1

2 (correct)

√2

What is the value of tan 45°?

1/√3

√3

0

1 (correct)

For a 30°-60°-90° triangle, what is the length of the side opposite 60°?

√2

√3 (correct)

2

1

If the lengths of two sides of a right triangle are known, which method should you use to find one of the angles?

Use trigonometric ratios Signup and view all the answers

If sin θ = 1/2, what angle does θ represent?

30° Signup and view all the answers

Which of the following represents the correct cosine ratio for 60°?

√3/2 Signup and view all the answers

What occurs when the values of a trigonometric function exceed its defined limits?

It may result in an undefined solution. Signup and view all the answers

If point P has coordinates (2, 3), what is the tangent of the angle A formed with the positive x-axis?

3/2 Signup and view all the answers

What is the relationship between angles A and B in point Q(-2, 3) in terms of α?

B + α = 180° Signup and view all the answers

In the Cartesian plane, the angle θ is formed between a line and which axis?

positive x-axis Signup and view all the answers

What must be true for two triangles to be considered similar?

Their corresponding angles are equal. Signup and view all the answers

Which of the following sets of angles can belong to similar triangles?

30°, 60°, 90° Signup and view all the answers

If triangle ABC is similar to triangle DEF, which of the following is true?

AC/DF = AB/DE Signup and view all the answers

What is the ratio of corresponding sides in similar triangles if the sides are respectively 4, 5, and 6 in one triangle and x, 5x/6, and 5x/4 in another?

2:3 Signup and view all the answers

Which property of similar triangles allows the definition of trigonometric ratios?

Proportional sides based on angle measurements. Signup and view all the answers

How does changing the size of a triangle affect the ratios of its sides?

Ratios remain the same. Signup and view all the answers

In the ratio of sides of similar triangles, what remains constant?

The proportional relationship among the sides. Signup and view all the answers

What information does the notation ΔABC ∼ ΔDEF provide about the corresponding angles?

Angle A is equal to Angle D. Signup and view all the answers

What is the formula for the sine of angle θ in a right-angled triangle?

$rac{ ext{opposite}}{ ext{hypotenuse}}$ Signup and view all the answers

Which of the following represents the tangent of angle θ?

$rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

Which reciprocal ratio corresponds to sine?

cosecant Signup and view all the answers

If you know the value of $ an heta$, how can you find $ ext{cot } heta$?

$rac{1}{ an heta}$ Signup and view all the answers

Which of the following statements regarding cosecant is true?

cosec θ = $rac{ ext{hypotenuse}}{ ext{opposite}}$ Signup and view all the answers

What must a calculator be set to in order to compute trigonometric ratios accurately?

Degrees mode Signup and view all the answers

Which of the following relationships between trigonometric functions is correct?

$ an heta imes ext{cot } heta = 1$ Signup and view all the answers

What is the relationship between cosine and secant?

sec θ = $rac{1}{ ext{cos } θ}$ Signup and view all the answers

For which angles can the values of sine, cosine, and tangent be easily calculated without a calculator?

Only special angles Signup and view all the answers

Which trigonometric ratio is defined as $rac{ ext{hypotenuse}}{ ext{adjacent}}$?

secant Signup and view all the answers

In which quadrant are all trigonometric ratios positive?

Quadrant I Signup and view all the answers

Which of the following is the correct value of $ an 60^ heta$?

$ ext{sqrt{3}}$ Signup and view all the answers

What is the value of $ an 90^ heta$?

$ ext{undefined}$ Signup and view all the answers

In the CAST diagram, which trigonometric ratios are positive in Quadrant II?

$ ext{sin} heta$ and $ ext{cosec} heta$ Signup and view all the answers

What is the definition of $ an heta$ in a right-angled triangle?

$rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

What is the angle of elevation?

The angle above the horizontal line to an object above Signup and view all the answers

What is the sine value of $30^ heta$?

$rac{1}{2}$ Signup and view all the answers

What is the relationship between the angle of elevation and angle of depression from the same point?

They are equal Signup and view all the answers

What must be true for two triangles to be classified as similar?

Their corresponding angles are equal. Signup and view all the answers

Which statement correctly explains the property of corresponding sides in similar triangles?

The ratios of corresponding sides remain proportional regardless of their lengths. Signup and view all the answers

What is the significance of labeling the vertices of similar triangles in order?

It ensures that the angles are matched correctly. Signup and view all the answers

In similar triangles, the relationship of which of the following properties is true?

The sum of angles in each triangle is 180°. Signup and view all the answers

For the triangles ΔABC and ΔDEF to maintain similarity, which of the following must hold?

$rac{AB}{DE} = rac{BC}{EF}$ must be true. Signup and view all the answers

If two triangles are similar, what can be concluded about their corresponding angles?

They are equal in measure. Signup and view all the answers

What does the similarity notation ΔABC ∼ ΔDEF imply?

Angle A is congruent to angle D. Signup and view all the answers

What is the significance of the angle measures 30°, 60°, and 90° in similar triangles?

They form the basis for defining all trigonometric ratios. Signup and view all the answers

In which quadrant of the Cartesian plane are only the sine and cosecant trigonometric ratios positive?

Quadrant II Signup and view all the answers

Which of the following statements about trigonometric ratios is true?

The cosine of an angle in Quadrant III is negative. Signup and view all the answers

Which trigonometric ratio represents the ratio of the length of the side adjacent to the angle to the length of the hypotenuse?

cosine Signup and view all the answers

What is the reciprocal of the sine function?

cosecant Signup and view all the answers

If the angle of elevation from a point is equal to 30°, what is the angle of depression from the same point?

60° Signup and view all the answers

What is the value of $ an 0^ heta$?

0 Signup and view all the answers

What must be true for the angles of a right triangle to be labeled as such?

It must have one angle equal to 90°. Signup and view all the answers

For which angle is the sine value equal to $rac{1}{2}$?

30° Signup and view all the answers

If you know the value of $ an heta$, how can you calculate $ ext{cot } heta$?

Take the reciprocal of $ an heta$. Signup and view all the answers

Which of the following relationships between sine and cosecant is correct?

$ ext{cosec } heta = rac{1}{ ext{sin } heta}$ Signup and view all the answers

Which of the following equations represents the ratio of sine and cosine for an arbitrary angle θ?

$\tan \theta = \frac{\sin \theta}{\cos \theta}$ Signup and view all the answers

Which trigonometric function is undefined at an angle of 90°?

Tangent Signup and view all the answers

Which of the following mnemonics correctly represents the definitions of the three primary trigonometric ratios?

Soh Cah Toa Signup and view all the answers

If a right triangle has an opposite side of length 3 and a hypotenuse of length 5, what is the value of $rac{3}{5}$ corresponding to?

$\sin \theta$ Signup and view all the answers

Which statement about the special angles for trigonometric ratios is true?

They can be calculated without a calculator. Signup and view all the answers

Which trigonometric function is defined as $rac{ ext{opposite}}{ ext{adjacent}}$?

tangent Signup and view all the answers

In a 30°-60°-90° triangle, what is the length of the side opposite the 30° angle if the hypotenuse is 4?

2 Signup and view all the answers

When using a calculator to find the trigonometric ratios, what setting must it typically be in?

Degrees mode Signup and view all the answers

What is the correct value of sin 60°?

√3/2 Signup and view all the answers

What is the primary function of the relationships $ ext{sin } heta imes ext{cosec } heta = 1$?

To indicate the relationship between reciprocal functions. Signup and view all the answers

If tan θ = 1 and θ is in the first quadrant, what is the value of θ?

45° Signup and view all the answers

For angle A formed by the coordinates P(2, 3), what is the calculated tangent ratio?

3/2 Signup and view all the answers

What angle corresponds to a cosine value of 1/2?

60° Signup and view all the answers

When using inverse trigonometric functions, what must the calculated value of sin θ be less than or equal to?

1 Signup and view all the answers

In a 45°-45°-90° triangle, what is the length of each leg if the hypotenuse is √2?

1 Signup and view all the answers

Which of the following is true regarding the angle B formed with the negative x-axis for point Q(-2, 3)?

B = 123.7° Signup and view all the answers

What is the tangent of angle θ in a triangle where the opposite side is 4 and the adjacent side is 3?

4/3 Signup and view all the answers

If angle θ is defined in the Cartesian plane, which method should be used to find θ using point P(2, 3)?

Use inverse tangent function Signup and view all the answers

What must be true about the corresponding angles in similar triangles?

They must be equal. Signup and view all the answers

Which of the following correctly describes the ratios of the sides of similar triangles?

They remain constant regardless of the triangles' dimensions. Signup and view all the answers

Given that two triangles are similar, how is the order of the vertices significant?

It establishes which angles correspond with each other. Signup and view all the answers

If triangle ABC is similar to triangle DEF, which proportion statement is true?

$rac{AB}{DE} = rac{BC}{EF}$ Signup and view all the answers

In the context of similar triangles, what does the notation ΔABC ∼ ΔDEF imply?

The triangles have the same shape but different sizes. Signup and view all the answers

Which statement correctly explains the concept of proportional sides in similar triangles?

The ratio of corresponding sides remains constant across all similar triangles. Signup and view all the answers

How can the ratios of the sides of a 30°-60°-90° triangle be described?

They remain consistent across any triangle of the same angles. Signup and view all the answers

Which statement about the similarity of triangles is false?

The ratios of corresponding sides must always be different. Signup and view all the answers

In Quadrant III of the CAST diagram, which trigonometric ratios are positive?

Tan and Cot Signup and view all the answers

What is the sine of 60° expressed in ratio form?

$rac{ ext{sqrt{3}}}{2}$ Signup and view all the answers

If the angle of depression from a point is 45°, what is the corresponding angle of elevation from the same point?

45° Signup and view all the answers

For a right triangle where the opposite side to angle theta is 4 and the hypotenuse is 8, what is the value of sine theta?

$rac{1}{2}$ Signup and view all the answers

Which of the following ratios describes cosecant?

$rac{r}{y}$ Signup and view all the answers

What is the tangent of 90°?

$ ext{Undefined}$ Signup and view all the answers

Which of the following statements is true regarding special angle values?

The tangent value at 30° is $rac{1}{ ext{sqrt{3}}}$. Signup and view all the answers

In which quadrant do sine and cosecant only have negative values?

Quadrant III Signup and view all the answers

Which of the following expressions correctly represents the relationship between the sine and cosecant of an angle?

$ ext{sine } heta imes ext{cosec } heta = 1$ Signup and view all the answers

If a right-angled triangle has an angle of $45^ heta$, which of the following is true regarding the lengths of the sides?

The opposite and adjacent sides are equal. Signup and view all the answers

Which of the following pairs of trigonometric ratios represents the correct set of reciprocals?

cos and sec Signup and view all the answers

In a right-angled triangle, which of the following ratios directly reflects the definition of tangent?

$ an heta = rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

What is the correct expression relating cotangent to tangent?

$ ext{cot } heta = rac{1}{ an heta}$ Signup and view all the answers

For an angle of $30^ heta$, which value corresponds to the cosine ratio?

$rac{ ext{adjacent}}{ ext{hypotenuse}}$ Signup and view all the answers

Which of the following conditions must hold true for the special angle ratios of 30°, 45°, and 60°?

They yield simple fractional values. Signup and view all the answers

Which statement correctly explains the use of a calculator for trigonometric calculations?

Ensure the calculator is in degrees mode for proper calculations. Signup and view all the answers

Given the relationship $sin^2 heta + cos^2 heta = 1$, which statement is true?

This equation is valid for all angles. Signup and view all the answers

Without a calculator, what is the sine value for the angle of $90^ heta$?

1 Signup and view all the answers

What is the length of the hypotenuse in a 45°-45°-90° triangle if each leg has a length of 1?

√2 Signup and view all the answers

Which of the following statements is true about the angles in triangle P(-2, 3)?

Angle B is supplementary to angle A. Signup and view all the answers

For which of the following values of θ does the sine function exceed its defined limit?

2 Signup and view all the answers

If the values of cosine ratio for 30°, 45°, and 60° are calculated, which of the following pairings is incorrect?

45° : 1/2 Signup and view all the answers

When finding an angle using the sine function, if sin θ = √3/2, what angle could θ possibly represent?

120° Signup and view all the answers

What is the correct expression to calculate the tangent ratio at point Q(-2, 3)?

tan A = -3/2 Signup and view all the answers

Which of the following represents a valid cosine ratio for the angle formed between the line drawing from the origin to the point P(2, 3)?

cos A = 2/√13 Signup and view all the answers

How would you isolate the sine ratio in the equation sin θ = 1/2 when finding the angle?

sin^-1(1/2) Signup and view all the answers

Which statement about the angles within a 30°-60°-90° triangle is false?

The opposite side to 30° is √3. Signup and view all the answers

What is the relationship between the sides of similar triangles?

The ratios of their corresponding sides remain constant. Signup and view all the answers

If triangles ΔABC and ΔDEF are similar, what must be true about their angles?

The corresponding angles are equal. Signup and view all the answers

Why is the order of labeling vertices important in similar triangles?

It shows the relationship between corresponding angles. Signup and view all the answers

In a set of similar triangles with consistently maintained angles, what happens to the side lengths as the triangle size increases?

The ratios of the corresponding sides remain proportional. Signup and view all the answers

Which of the following correctly describes the proportionality of sides in a 30°-60°-90° triangle?

The sides have a fixed ratio of 1:$ ext{√3}$:2. Signup and view all the answers

What must be true for two triangles to be labeled similar in notation?

Corresponding angles must be equal, and sides are proportional. Signup and view all the answers

Which of the following is a general rule regarding the sides of similar triangles?

The longest side must always be opposite the smallest angle. Signup and view all the answers

How are the properties of similar triangles foundational to trigonometry?

Similar triangles provide consistent ratios to define trigonometric functions. Signup and view all the answers

What is the approximate value of tan 30°?

√3/3 Signup and view all the answers

In a 45°-45°-90° triangle, what ratio represents the relationship between the legs and the hypotenuse?

1:√2 Signup and view all the answers

For the triangle formed by point P(2, 3), what is the sine of angle A?

3/√13 Signup and view all the answers

If solving for an angle with cos θ = 1/2, which angle(s) can θ represent?

60° or 300° Signup and view all the answers

What is the value of sin 60°?

√3/2 Signup and view all the answers

How would you calculate angle B in triangle Q(-2, 3) if tan α = 3/2?

180° - 56.3° Signup and view all the answers

In the context of trigonometric functions, what does the symbol sin^-1 denote?

Inverse sine function Signup and view all the answers

If a point is plotted at coordinates (0, 1), which trigonometric ratio defines the angle formed with the positive x-axis?

sin θ = 1 Signup and view all the answers

What condition must be met for a trigonometric function value to have no solution?

|sin θ| > 1 Signup and view all the answers

When dealing with a 30°-60°-90° triangle, what is the relationship of the lengths of the sides?

Hypotenuse is twice the length of opposite 30° Signup and view all the answers

What is the value of $ an 30^ heta$?

$rac{1}{ ho}$ Signup and view all the answers

In which quadrant are only tangent and cotangent positive according to the CAST diagram?

Quadrant III Signup and view all the answers

Which of the following correctly defines cosecant in terms of the sides of a right triangle?

$rac{ ext{hypotenuse}}{ ext{opposite}}$ Signup and view all the answers

What is the sine value of an angle of $90^ heta$?

1 Signup and view all the answers

Which of the following relationships is true regarding angles of elevation and depression?

The angle of elevation from one point is equal to the angle of depression from the corresponding point. Signup and view all the answers

What does the CAST diagram signify about Quadrant II?

Only sine and cosecant are positive. Signup and view all the answers

If $ an heta = rac{1}{ ho}$, what can be concluded about angle $ heta$?

It is equal to $30^ heta$. Signup and view all the answers

What does the notation of two triangles being similar, ΔABC ∼ ΔDEF, imply about their angles?

Their angles are equal but their sides are unequal. Signup and view all the answers

What is the correct definition of the cosecant function?

The ratio of the hypotenuse to the opposite side Signup and view all the answers

Which of the following statements about the tangent function is true?

It represents the ratio of the opposite side to the adjacent side. Signup and view all the answers

For which of the following angles can sine, cosine, and tangent values be easily computed without a calculator?

30°, 45°, and 60° Signup and view all the answers

What would be the cosecant of an angle if its sine value is 3/4?

4/3 Signup and view all the answers

Which relationship correctly defines cosine in terms of triangle sides?

cosine is the adjacent side divided by the hypotenuse Signup and view all the answers

If $ an heta = 5$, what value corresponds to $ ext{cot } heta$?

1/5 Signup and view all the answers

Which expression correctly indicates a relationship involving sine and cosecant?

$ ext{sin } heta imes ext{cosec } heta = 1$ Signup and view all the answers

If a triangle has angles measuring 30°, 60°, and 90°, what is the sine of the 30° angle?

$rac{1}{2}$ Signup and view all the answers

What value is represented by the secant function if $ heta = 45°$?

$ ext{sqrt}(2)$ Signup and view all the answers

What must be true about the angles in a right triangle for their sine values to be calculated?

The angles must be less than 90° Signup and view all the answers

Which trigonometric ratio is equal to the ratio of the hypotenuse to the opposite side?

Cosecant Signup and view all the answers

In which quadrant is the cosine ratio negative?

Quadrant III Signup and view all the answers

What is the value of sin 90°?

1 Signup and view all the answers

Which of the following statements accurately describes the angle of elevation?

It is the angle from the horizontal line to an object above. Signup and view all the answers

What is the relationship between sine and cosecant?

Cosecant is the reciprocal of sine. Signup and view all the answers

In the CAST diagram, which quadrant has only tangent and cotangent as positive?

Quadrant III Signup and view all the answers

What is the sine value of 30°?

1/2 Signup and view all the answers

Which of the following angles has a tangent value that is undefined?

90° Signup and view all the answers

What condition must two triangles satisfy to be classified as similar?

Their angles must be equal. Signup and view all the answers

How does the size of a triangle impact the ratios of similar triangles?

The ratios remain constant despite changes in size. Signup and view all the answers

Which of the following statements correctly represents the relationship of sides in two similar triangles?

$rac{AB}{DE} = rac{BC}{EF}$ Signup and view all the answers

What must be indicated by the notation ΔABC ∼ ΔDEF?

The corresponding angles of triangle ABC are equal to those in triangle DEF. Signup and view all the answers

Which property is not true for similar triangles?

All sides are equal in length. Signup and view all the answers

In similar triangles, which of the following ratios remains constant?

The ratios of corresponding sides. Signup and view all the answers

What is the significance of the angles 30°, 60°, and 90° in triangles?

They are the angles in right triangles that lead to specific side ratios. Signup and view all the answers

Which statement describes the relationship of corresponding angles in similar triangles?

They are equal. Signup and view all the answers

In a 30°-60°-90° triangle, what is the relationship between the lengths of the sides?

Hypotenuse is double the length of the side opposite 30°. Signup and view all the answers

What is the tangent value for the angle 60°?

$ oot 3$ Signup and view all the answers

When using trigonometric ratios to determine an angle, which function is applied to a ratio of $rac{3}{2}$?

tangent inverse Signup and view all the answers

What is the sine of angle θ if $ an heta = rac{ oot 3}{3}$?

$rac{1}{2}$ Signup and view all the answers

For the point Q at (-2, 3), which of the following correctly describes angle B formed with the positive x-axis?

B = 180° - α Signup and view all the answers

If the sine of angle θ is 1/2, which angle could θ represent?

30° Signup and view all the answers

When finding angles in the Cartesian plane, what is necessary for accurate calculations?

Trigonometric ratios must not exceed their defined limits. Signup and view all the answers

In solving the equation for the angle θ where sin θ = y/r, which expression correctly rearranges the equation?

θ = sin^{-1}(y/r) Signup and view all the answers

In a right triangle, if the hypotenuse is less than either of the other two sides, which conclusion can be drawn?

This is not a valid triangle. Signup and view all the answers

What is the value of the cosecant function in terms of the sine function?

cosec $ heta$ = $rac{1}{ ext{sin } heta}$ Signup and view all the answers

Which of the following correctly defines the cosine function?

cos $ heta$ = $rac{ ext{adjacent}}{ ext{hypotenuse}}$ Signup and view all the answers

What is the relationship represented by the equation sin $ heta$ × cosec $ heta$?

sin $ heta$ × cosec $ heta$ = 1 Signup and view all the answers

Which of the following represents the tangent function?

tan $ heta$ = $rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

How can a calculator be utilized to find sec $ heta$?

Calculate $rac{1}{ ext{cos } heta}$ Signup and view all the answers

What is the definition of cosecant in terms of a right-angled triangle?

cosec $ heta$ = $rac{ ext{hypotenuse}}{ ext{opposite}}$ Signup and view all the answers

Which statement is true regarding special angles in trigonometry?

Only 0°, 30°, 60°, and 90° yield simple trigonometric values. Signup and view all the answers

Which of the following defines the secant function in terms of cosine?

sec $ heta$ = $rac{1}{ ext{cos } heta}$ Signup and view all the answers

What must a calculator be set to in order to compute trigonometric ratios accurately?

Degrees mode Signup and view all the answers

Which of the following expressions correctly represents the tangent of an angle?

tan $ heta$ = $rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

Gr 10 Math Ch 4 SUM: Trigonometry

Questions and Answers

What is the length of the hypotenuse in a 30°-60°-90° triangle?

What is the value of tan 45°?

For a 30°-60°-90° triangle, what is the length of the side opposite 60°?

If the lengths of two sides of a right triangle are known, which method should you use to find one of the angles?

If sin θ = 1/2, what angle does θ represent?

Which of the following represents the correct cosine ratio for 60°?

What occurs when the values of a trigonometric function exceed its defined limits?

If point P has coordinates (2, 3), what is the tangent of the angle A formed with the positive x-axis?

What is the relationship between angles A and B in point Q(-2, 3) in terms of α?

In the Cartesian plane, the angle θ is formed between a line and which axis?

What must be true for two triangles to be considered similar?

Which of the following sets of angles can belong to similar triangles?

If triangle ABC is similar to triangle DEF, which of the following is true?

What is the ratio of corresponding sides in similar triangles if the sides are respectively 4, 5, and 6 in one triangle and x, 5x/6, and 5x/4 in another?

Which property of similar triangles allows the definition of trigonometric ratios?

How does changing the size of a triangle affect the ratios of its sides?

In the ratio of sides of similar triangles, what remains constant?

What information does the notation ΔABC ∼ ΔDEF provide about the corresponding angles?

What is the formula for the sine of angle θ in a right-angled triangle?

Which of the following represents the tangent of angle θ?

Which reciprocal ratio corresponds to sine?

If you know the value of $ an heta$, how can you find $ ext{cot } heta$?

Which of the following statements regarding cosecant is true?

What must a calculator be set to in order to compute trigonometric ratios accurately?

Which of the following relationships between trigonometric functions is correct?

What is the relationship between cosine and secant?

For which angles can the values of sine, cosine, and tangent be easily calculated without a calculator?

Which trigonometric ratio is defined as $ rac{ ext{hypotenuse}}{ ext{adjacent}}$?

In which quadrant are all trigonometric ratios positive?

Which of the following is the correct value of $ an 60^ heta$?

What is the value of $ an 90^ heta$?

In the CAST diagram, which trigonometric ratios are positive in Quadrant II?

What is the definition of $ an heta$ in a right-angled triangle?

What is the angle of elevation?

What is the sine value of $30^ heta$?

What is the relationship between the angle of elevation and angle of depression from the same point?

What must be true for two triangles to be classified as similar?

Which statement correctly explains the property of corresponding sides in similar triangles?

What is the significance of labeling the vertices of similar triangles in order?

In similar triangles, the relationship of which of the following properties is true?

For the triangles ΔABC and ΔDEF to maintain similarity, which of the following must hold?

If two triangles are similar, what can be concluded about their corresponding angles?

What does the similarity notation ΔABC ∼ ΔDEF imply?

What is the significance of the angle measures 30°, 60°, and 90° in similar triangles?

In which quadrant of the Cartesian plane are only the sine and cosecant trigonometric ratios positive?

Which of the following statements about trigonometric ratios is true?

Which trigonometric ratio represents the ratio of the length of the side adjacent to the angle to the length of the hypotenuse?

What is the reciprocal of the sine function?

If the angle of elevation from a point is equal to 30°, what is the angle of depression from the same point?

What is the value of $ an 0^ heta$?

What must be true for the angles of a right triangle to be labeled as such?

For which angle is the sine value equal to $ rac{1}{2}$?

If you know the value of $ an heta$, how can you calculate $ ext{cot } heta$?

Which of the following relationships between sine and cosecant is correct?

Which of the following equations represents the ratio of sine and cosine for an arbitrary angle θ?

Which trigonometric function is undefined at an angle of 90°?

Which of the following mnemonics correctly represents the definitions of the three primary trigonometric ratios?

If a right triangle has an opposite side of length 3 and a hypotenuse of length 5, what is the value of $ rac{3}{5}$ corresponding to?

Which statement about the special angles for trigonometric ratios is true?

Which trigonometric function is defined as $ rac{ ext{opposite}}{ ext{adjacent}}$?

In a 30°-60°-90° triangle, what is the length of the side opposite the 30° angle if the hypotenuse is 4?

When using a calculator to find the trigonometric ratios, what setting must it typically be in?

What is the correct value of sin 60°?

What is the primary function of the relationships $ ext{sin } heta imes ext{cosec } heta = 1$?

If tan θ = 1 and θ is in the first quadrant, what is the value of θ?

For angle A formed by the coordinates P(2, 3), what is the calculated tangent ratio?

What angle corresponds to a cosine value of 1/2?

When using inverse trigonometric functions, what must the calculated value of sin θ be less than or equal to?

In a 45°-45°-90° triangle, what is the length of each leg if the hypotenuse is √2?

Which of the following is true regarding the angle B formed with the negative x-axis for point Q(-2, 3)?

What is the tangent of angle θ in a triangle where the opposite side is 4 and the adjacent side is 3?

If angle θ is defined in the Cartesian plane, which method should be used to find θ using point P(2, 3)?

What must be true about the corresponding angles in similar triangles?

Which of the following correctly describes the ratios of the sides of similar triangles?

Given that two triangles are similar, how is the order of the vertices significant?

If triangle ABC is similar to triangle DEF, which proportion statement is true?

In the context of similar triangles, what does the notation ΔABC ∼ ΔDEF imply?

Which statement correctly explains the concept of proportional sides in similar triangles?

Which trigonometric ratio is defined as $rac{ ext{hypotenuse}}{ ext{adjacent}}$?

For which angle is the sine value equal to $rac{1}{2}$?

If a right triangle has an opposite side of length 3 and a hypotenuse of length 5, what is the value of $rac{3}{5}$ corresponding to?

Which trigonometric function is defined as $rac{ ext{opposite}}{ ext{adjacent}}$?