Podcast
Questions and Answers
What is the length of the hypotenuse in a 30°-60°-90° triangle?
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°?
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°?
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?
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?
If sin θ = 1/2, what angle does θ represent?
Which of the following represents the correct cosine ratio for 60°?
Which of the following represents the correct cosine ratio for 60°?
What occurs when the values of a trigonometric function exceed its defined limits?
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?
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?
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?
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?
What must be true for two triangles to be considered similar?
Which of the following sets of angles can belong to similar triangles?
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?
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?
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?
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?
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?
In the ratio of sides of similar triangles, what remains constant?
What information does the notation ΔABC ∼ ΔDEF provide about the corresponding angles?
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?
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 of the following represents the tangent of angle θ?
Which reciprocal ratio corresponds to sine?
Which reciprocal ratio corresponds to sine?
If you know the value of $ an heta$, how can you find $ ext{cot } heta$?
If you know the value of $ an heta$, how can you find $ ext{cot } heta$?
Which of the following statements regarding cosecant is true?
Which of the following statements regarding cosecant is true?
What must a calculator be set to in order to compute trigonometric ratios accurately?
What must a calculator be set to in order to compute trigonometric ratios accurately?
Which of the following relationships between trigonometric functions is correct?
Which of the following relationships between trigonometric functions is correct?
What is the relationship between cosine and secant?
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?
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}}$?
Which trigonometric ratio is defined as $ rac{ ext{hypotenuse}}{ ext{adjacent}}$?
In which quadrant are all trigonometric ratios positive?
In which quadrant are all trigonometric ratios positive?
Which of the following is the correct value of $ an 60^ heta$?
Which of the following is the correct value of $ an 60^ heta$?
What is the value of $ an 90^ heta$?
What is the value of $ an 90^ heta$?
In the CAST diagram, which trigonometric ratios are positive in Quadrant II?
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 definition of $ an heta$ in a right-angled triangle?
What is the angle of elevation?
What is the angle of elevation?
What is the sine value of $30^ heta$?
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 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?
What must be true for two triangles to be classified as similar?
Which statement correctly explains the property of corresponding sides in similar triangles?
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?
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?
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?
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?
If two triangles are similar, what can be concluded about their corresponding angles?
What does the similarity notation ΔABC ∼ ΔDEF imply?
What does the similarity notation ΔABC ∼ ΔDEF imply?
What is the significance of the angle measures 30°, 60°, and 90° in similar triangles?
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?
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 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?
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?
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?
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 is the value of $ an 0^ heta$?
What must be true for the angles of a right triangle to be labeled as such?
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}$?
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$?
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 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 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 trigonometric function is undefined at an angle of 90°?
Which of the following mnemonics correctly represents the definitions of the three primary trigonometric ratios?
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?
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 statement about the special angles for trigonometric ratios is true?
Which trigonometric function is defined as $ rac{ ext{opposite}}{ ext{adjacent}}$?
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?
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?
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 correct value of sin 60°?
What is the primary function of the relationships $ ext{sin } heta imes ext{cosec } heta = 1$?
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?
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?
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?
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?
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?
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)?
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?
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)?
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?
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?
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?
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?
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?
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 statement correctly explains the concept of proportional sides in similar triangles?
How can the ratios of the sides of a 30°-60°-90° triangle be described?
How can the ratios of the sides of a 30°-60°-90° triangle be described?
Which statement about the similarity of triangles is false?
Which statement about the similarity of triangles is false?
In Quadrant III of the CAST diagram, which trigonometric ratios are positive?
In Quadrant III of the CAST diagram, which trigonometric ratios are positive?
What is the sine of 60° expressed in ratio form?
What is the sine of 60° expressed in ratio form?
If the angle of depression from a point is 45°, what is the corresponding angle of elevation from the same point?
If the angle of depression from a point is 45°, what is the corresponding angle of elevation from the same point?
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?
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?
Which of the following ratios describes cosecant?
Which of the following ratios describes cosecant?
What is the tangent of 90°?
What is the tangent of 90°?
Which of the following statements is true regarding special angle values?
Which of the following statements is true regarding special angle values?
In which quadrant do sine and cosecant only have negative values?
In which quadrant do sine and cosecant only have negative values?
Which of the following expressions correctly represents the relationship between the sine and cosecant of an angle?
Which of the following expressions correctly represents the relationship between the sine and cosecant of an angle?
If a right-angled triangle has an angle of $45^ heta$, which of the following is true regarding the lengths of the sides?
If a right-angled triangle has an angle of $45^ heta$, which of the following is true regarding the lengths of the sides?
Which of the following pairs of trigonometric ratios represents the correct set of reciprocals?
Which of the following pairs of trigonometric ratios represents the correct set of reciprocals?
In a right-angled triangle, which of the following ratios directly reflects the definition of tangent?
In a right-angled triangle, which of the following ratios directly reflects the definition of tangent?
What is the correct expression relating cotangent to tangent?
What is the correct expression relating cotangent to tangent?
For an angle of $30^ heta$, which value corresponds to the cosine ratio?
For an angle of $30^ heta$, which value corresponds to the cosine ratio?
Which of the following conditions must hold true for the special angle ratios of 30°, 45°, and 60°?
Which of the following conditions must hold true for the special angle ratios of 30°, 45°, and 60°?
Which statement correctly explains the use of a calculator for trigonometric calculations?
Which statement correctly explains the use of a calculator for trigonometric calculations?
Given the relationship $sin^2 heta + cos^2 heta = 1$, which statement is true?
Given the relationship $sin^2 heta + cos^2 heta = 1$, which statement is true?
Without a calculator, what is the sine value for the angle of $90^ heta$?
Without a calculator, what is the sine value for the angle of $90^ heta$?
What is the length of the hypotenuse in a 45°-45°-90° triangle if each leg has a length of 1?
What is the length of the hypotenuse in a 45°-45°-90° triangle if each leg has a length of 1?
Which of the following statements is true about the angles in triangle P(-2, 3)?
Which of the following statements is true about the angles in triangle P(-2, 3)?
For which of the following values of θ does the sine function exceed its defined limit?
For which of the following values of θ does the sine function exceed its defined limit?
If the values of cosine ratio for 30°, 45°, and 60° are calculated, which of the following pairings is incorrect?
If the values of cosine ratio for 30°, 45°, and 60° are calculated, which of the following pairings is incorrect?
When finding an angle using the sine function, if sin θ = √3/2, what angle could θ possibly represent?
When finding an angle using the sine function, if sin θ = √3/2, what angle could θ possibly represent?
What is the correct expression to calculate the tangent ratio at point Q(-2, 3)?
What is the correct expression to calculate the tangent ratio at point Q(-2, 3)?
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)?
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)?
How would you isolate the sine ratio in the equation sin θ = 1/2 when finding the angle?
How would you isolate the sine ratio in the equation sin θ = 1/2 when finding the angle?
Which statement about the angles within a 30°-60°-90° triangle is false?
Which statement about the angles within a 30°-60°-90° triangle is false?
What is the relationship between the sides of similar triangles?
What is the relationship between the sides of similar triangles?
If triangles ΔABC and ΔDEF are similar, what must be true about their angles?
If triangles ΔABC and ΔDEF are similar, what must be true about their angles?
Why is the order of labeling vertices important in similar triangles?
Why is the order of labeling vertices important in similar triangles?
In a set of similar triangles with consistently maintained angles, what happens to the side lengths as the triangle size increases?
In a set of similar triangles with consistently maintained angles, what happens to the side lengths as the triangle size increases?
Which of the following correctly describes the proportionality of sides in a 30°-60°-90° triangle?
Which of the following correctly describes the proportionality of sides in a 30°-60°-90° triangle?
What must be true for two triangles to be labeled similar in notation?
What must be true for two triangles to be labeled similar in notation?
Which of the following is a general rule regarding the sides of similar triangles?
Which of the following is a general rule regarding the sides of similar triangles?
How are the properties of similar triangles foundational to trigonometry?
How are the properties of similar triangles foundational to trigonometry?
What is the approximate value of tan 30°?
What is the approximate value of tan 30°?
In a 45°-45°-90° triangle, what ratio represents the relationship between the legs and the hypotenuse?
In a 45°-45°-90° triangle, what ratio represents the relationship between the legs and the hypotenuse?
For the triangle formed by point P(2, 3), what is the sine of angle A?
For the triangle formed by point P(2, 3), what is the sine of angle A?
If solving for an angle with cos θ = 1/2, which angle(s) can θ represent?
If solving for an angle with cos θ = 1/2, which angle(s) can θ represent?
What is the value of sin 60°?
What is the value of sin 60°?
How would you calculate angle B in triangle Q(-2, 3) if tan α = 3/2?
How would you calculate angle B in triangle Q(-2, 3) if tan α = 3/2?
In the context of trigonometric functions, what does the symbol sin^-1 denote?
In the context of trigonometric functions, what does the symbol sin^-1 denote?
If a point is plotted at coordinates (0, 1), which trigonometric ratio defines the angle formed with the positive x-axis?
If a point is plotted at coordinates (0, 1), which trigonometric ratio defines the angle formed with the positive x-axis?
What condition must be met for a trigonometric function value to have no solution?
What condition must be met for a trigonometric function value to have no solution?
When dealing with a 30°-60°-90° triangle, what is the relationship of the lengths of the sides?
When dealing with a 30°-60°-90° triangle, what is the relationship of the lengths of the sides?
What is the value of $ an 30^ heta$?
What is the value of $ an 30^ heta$?
In which quadrant are only tangent and cotangent positive according to the CAST diagram?
In which quadrant are only tangent and cotangent positive according to the CAST diagram?
Which of the following correctly defines cosecant in terms of the sides of a right triangle?
Which of the following correctly defines cosecant in terms of the sides of a right triangle?
What is the sine value of an angle of $90^ heta$?
What is the sine value of an angle of $90^ heta$?
Which of the following relationships is true regarding angles of elevation and depression?
Which of the following relationships is true regarding angles of elevation and depression?
What does the CAST diagram signify about Quadrant II?
What does the CAST diagram signify about Quadrant II?
If $ an heta = rac{1}{
ho}$, what can be concluded about angle $ heta$?
If $ an heta = rac{1}{ ho}$, what can be concluded about angle $ heta$?
What does the notation of two triangles being similar, ΔABC ∼ ΔDEF, imply about their angles?
What does the notation of two triangles being similar, ΔABC ∼ ΔDEF, imply about their angles?
What is the correct definition of the cosecant function?
What is the correct definition of the cosecant function?
Which of the following statements about the tangent function is true?
Which of the following statements about the tangent function is true?
For which of the following angles can sine, cosine, and tangent values be easily computed without a calculator?
For which of the following angles can sine, cosine, and tangent values be easily computed without a calculator?
What would be the cosecant of an angle if its sine value is 3/4?
What would be the cosecant of an angle if its sine value is 3/4?
Which relationship correctly defines cosine in terms of triangle sides?
Which relationship correctly defines cosine in terms of triangle sides?
If $ an heta = 5$, what value corresponds to $ ext{cot } heta$?
If $ an heta = 5$, what value corresponds to $ ext{cot } heta$?
Which expression correctly indicates a relationship involving sine and cosecant?
Which expression correctly indicates a relationship involving sine and cosecant?
If a triangle has angles measuring 30°, 60°, and 90°, what is the sine of the 30° angle?
If a triangle has angles measuring 30°, 60°, and 90°, what is the sine of the 30° angle?
What value is represented by the secant function if $ heta = 45°$?
What value is represented by the secant function if $ heta = 45°$?
What must be true about the angles in a right triangle for their sine values to be calculated?
What must be true about the angles in a right triangle for their sine values to be calculated?
Which trigonometric ratio is equal to the ratio of the hypotenuse to the opposite side?
Which trigonometric ratio is equal to the ratio of the hypotenuse to the opposite side?
In which quadrant is the cosine ratio negative?
In which quadrant is the cosine ratio negative?
What is the value of sin 90°?
What is the value of sin 90°?
Which of the following statements accurately describes the angle of elevation?
Which of the following statements accurately describes the angle of elevation?
What is the relationship between sine and cosecant?
What is the relationship between sine and cosecant?
In the CAST diagram, which quadrant has only tangent and cotangent as positive?
In the CAST diagram, which quadrant has only tangent and cotangent as positive?
What is the sine value of 30°?
What is the sine value of 30°?
Which of the following angles has a tangent value that is undefined?
Which of the following angles has a tangent value that is undefined?
What condition must two triangles satisfy to be classified as similar?
What condition must two triangles satisfy to be classified as similar?
How does the size of a triangle impact the ratios of similar triangles?
How does the size of a triangle impact the ratios of similar triangles?
Which of the following statements correctly represents the relationship of sides in two similar triangles?
Which of the following statements correctly represents the relationship of sides in two similar triangles?
What must be indicated by the notation ΔABC ∼ ΔDEF?
What must be indicated by the notation ΔABC ∼ ΔDEF?
Which property is not true for similar triangles?
Which property is not true for similar triangles?
In similar triangles, which of the following ratios remains constant?
In similar triangles, which of the following ratios remains constant?
What is the significance of the angles 30°, 60°, and 90° in triangles?
What is the significance of the angles 30°, 60°, and 90° in triangles?
Which statement describes the relationship of corresponding angles in similar triangles?
Which statement describes the relationship of corresponding angles in similar triangles?
In a 30°-60°-90° triangle, what is the relationship between the lengths of the sides?
In a 30°-60°-90° triangle, what is the relationship between the lengths of the sides?
What is the tangent value for the angle 60°?
What is the tangent value for the angle 60°?
When using trigonometric ratios to determine an angle, which function is applied to a ratio of $ rac{3}{2}$?
When using trigonometric ratios to determine an angle, which function is applied to a ratio of $ rac{3}{2}$?
What is the sine of angle θ if $ an heta = rac{
oot 3}{3}$?
What is the sine of angle θ if $ an heta = rac{ oot 3}{3}$?
For the point Q at (-2, 3), which of the following correctly describes angle B formed with the positive x-axis?
For the point Q at (-2, 3), which of the following correctly describes angle B formed with the positive x-axis?
If the sine of angle θ is 1/2, which angle could θ represent?
If the sine of angle θ is 1/2, which angle could θ represent?
When finding angles in the Cartesian plane, what is necessary for accurate calculations?
When finding angles in the Cartesian plane, what is necessary for accurate calculations?
In solving the equation for the angle θ where sin θ = y/r, which expression correctly rearranges the equation?
In solving the equation for the angle θ where sin θ = y/r, which expression correctly rearranges the equation?
In a right triangle, if the hypotenuse is less than either of the other two sides, which conclusion can be drawn?
In a right triangle, if the hypotenuse is less than either of the other two sides, which conclusion can be drawn?
What is the value of the cosecant function in terms of the sine function?
What is the value of the cosecant function in terms of the sine function?
Which of the following correctly defines the cosine function?
Which of the following correctly defines the cosine function?
What is the relationship represented by the equation sin $ heta$ × cosec $ heta$?
What is the relationship represented by the equation sin $ heta$ × cosec $ heta$?
Which of the following represents the tangent function?
Which of the following represents the tangent function?
How can a calculator be utilized to find sec $ heta$?
How can a calculator be utilized to find sec $ heta$?
What is the definition of cosecant in terms of a right-angled triangle?
What is the definition of cosecant in terms of a right-angled triangle?
Which statement is true regarding special angles in trigonometry?
Which statement is true regarding special angles in trigonometry?
Which of the following defines the secant function in terms of cosine?
Which of the following defines the secant function in terms of cosine?
What must a calculator be set to in order to compute trigonometric ratios accurately?
What must a calculator be set to in order to compute trigonometric ratios accurately?
Which of the following expressions correctly represents the tangent of an angle?
Which of the following expressions correctly represents the tangent of an angle?
