Gr 10 Math Ch 4: Defining Ratios in the Cartesian Plane

What does the tangent ratio represent for a point in the Cartesian plane?

The angle between the line and the negative x-axis

The length of the line from the origin to the point

The ratio of the opposite side to the adjacent side of a right triangle (correct)

The ratio of the angle to the x-axis

If the coordinates of point P are (2, 3), what is the value of the tangent ratio used to find angle A?

$3 + 2$

$rac{3}{2}$ (correct)

$rac{2}{3}$

$rac{1}{rac{2}{3}}$

How is angle B related to angle α for the point Q(-2, 3)?

B and α are the same angle

B + α = 90^ ext{o}

B + α = 180^ ext{o} (correct)

B and α are complementary angles

What is the value of angle B when the coordinates for point Q(-2, 3) are used?

123.7^ ext{o} Signup and view all the answers

What is the radius of the circle centered at the origin if it passes through point P(2, 3)?

$ ext{sqrt}(2^2 + 3^2)$ Signup and view all the answers

Which statement about the angle θ formed by point P(x, y) and the x-axis is true?

θ is the angle between the line OP and the x-axis Signup and view all the answers

When working with the angle of a point in the fourth quadrant, how is the tangent ratio affected?

The tangent is always negative Signup and view all the answers

What relationship holds true between the angles formed with the positive and negative x-axes?

They are supplementary angles Signup and view all the answers

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

Quadrant II Signup and view all the answers

What is the value of $ an 45^ heta$?

1 Signup and view all the answers

Which trigonometric ratio is undefined at $90^ heta$?

$ an 90^ heta$ Signup and view all the answers

What is the sine of $30^ heta$?

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

What is the relationship between sine and cosecant?

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

Which of the following statements is true regarding the trigonometric functions in Quadrant IV?

Only cosine and secant are positive. Signup and view all the answers

Which trigonometric ratio is positive in Quadrant II?

sin θ Signup and view all the answers

What is the value of tan $60^ heta$?

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

Which of the following statements is true about cosecant?

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

For the angle $0^ heta$, what is the value of sin θ?

0 Signup and view all the answers

In which quadrant are tan θ and cot θ positively defined?

Quadrant III Signup and view all the answers

What is the cosine of angle $90^ heta$?

0 Signup and view all the answers

What is the value of the tangent ratio for angle A formed by the point P(2, 3)?

$1.5$ Signup and view all the answers

Which of the following angles represents angle B for point Q(-2, 3)?

$123.7^ heta$ Signup and view all the answers

If point P is located at (x, y) in the Cartesian plane, which formula represents the length from the origin to point P?

$ ext{length} = ext{sqrt}(x^2 + y^2)$ Signup and view all the answers

What relationship holds between angles A and B when considering point Q(-2, 3) and point P(2, 3)?

Angle B is the reflection of angle A across the x-axis. Signup and view all the answers

For a point located in the second quadrant, which statement about the tangent ratio is true?

The tangent is negative. Signup and view all the answers

Angle α for point Q(-2, 3) is formed with which axis?

The negative x-axis Signup and view all the answers

What is the measure of angle α given that $ an heta = rac{3}{2}$?

$56.3^ heta$ Signup and view all the answers

When plotting points in the Cartesian plane, which quadrant is characterized by positive x and negative y coordinates?

Quadrant IV Signup and view all the answers

Which trigonometric ratio is positive in Quadrant III?

tan θ Signup and view all the answers

What is the sine value of $45^ heta$?

$\frac{1}{\sqrt{2}}$ Signup and view all the answers

When the angle θ is $90^ heta$, what is the value of cos θ?

0 Signup and view all the answers

In which quadrant are only the cosine and secant trigonometric ratios positive?

Quadrant IV Signup and view all the answers

Which of the following statements is true regarding the tangent of $30^ heta$?

It equals $\frac{1}{\sqrt{3}}$. Signup and view all the answers

Which trigonometric ratio is defined as $\frac{y}{x}$?

tan θ Signup and view all the answers

If point Q is located at (-2, 3) in the Cartesian plane, what is the general formula to determine angle B formed between line OQ and the positive x-axis?

$B = 180^ heta - an^{-1}(3/2)$ Signup and view all the answers

What is the correct relationship between angle α and angle B when considering point Q(-2, 3) in the Cartesian plane?

$B + heta = 180^ heta$ Signup and view all the answers

When determining the angle θ formed by point P(2, 3) with the x-axis, which of the following represents the radius of the circle centered at the origin?

$r = ext{sqrt}(2^2 + 3^2)$ Signup and view all the answers

Which of the following statements correctly describes the coordinates of point P(2, 3) in relation to angle A?

The coordinates indicate that angle A is in the first quadrant. Signup and view all the answers

For angle B formed by point Q(-2, 3), which of the following correctly describes the tangent ratio in this case?

$ an B = rac{3}{-2}$ Signup and view all the answers

What would be the approximate degree measure of angle A formed at point P(2, 3)?

$36.9^ heta$ Signup and view all the answers

When plotting a point P(x, y) in relation to the radius r, which of the following statements is true?

The radius is determined by $r = ext{sqrt}(x^2 + y^2)$. Signup and view all the answers

In dealing with angles in the Cartesian plane, which statement correctly compares angles formed in the first and second quadrants?

Angle B is always the supplement of angle A. Signup and view all the answers

In which quadrant is the sine value positive and the tangent value undefined?

Quadrant II Signup and view all the answers

Given the angle $45^\circ$, what is the value of cosecant?

$\sqrt{2}$ Signup and view all the answers

Which trigonometric ratio is represented by the formula $\frac{r}{y}$?

cosecant Signup and view all the answers

What is the tangent value for angle $30^\circ$?

$\frac{1}{\sqrt{3}}$ Signup and view all the answers

For angles in Quadrant IV, which of the following trigonometric ratios is positive?

cosine Signup and view all the answers

Gr 10 Math Ch 4: Defining Ratios in the Cartesian Plane

Questions and Answers

What does the tangent ratio represent for a point in the Cartesian plane?

If the coordinates of point P are (2, 3), what is the value of the tangent ratio used to find angle A?

How is angle B related to angle α for the point Q(-2, 3)?

What is the value of angle B when the coordinates for point Q(-2, 3) are used?

What is the radius of the circle centered at the origin if it passes through point P(2, 3)?

Which statement about the angle θ formed by point P(x, y) and the x-axis is true?

When working with the angle of a point in the fourth quadrant, how is the tangent ratio affected?

What relationship holds true between the angles formed with the positive and negative x-axes?

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

What is the value of $ an 45^ heta$?

Which trigonometric ratio is undefined at $90^ heta$?

What is the sine of $30^ heta$?

What is the relationship between sine and cosecant?

Which of the following statements is true regarding the trigonometric functions in Quadrant IV?

Which trigonometric ratio is positive in Quadrant II?

What is the value of tan $60^ heta$?

Which of the following statements is true about cosecant?

For the angle $0^ heta$, what is the value of sin θ?

In which quadrant are tan θ and cot θ positively defined?

What is the cosine of angle $90^ heta$?

What is the value of the tangent ratio for angle A formed by the point P(2, 3)?

Which of the following angles represents angle B for point Q(-2, 3)?

If point P is located at (x, y) in the Cartesian plane, which formula represents the length from the origin to point P?

What relationship holds between angles A and B when considering point Q(-2, 3) and point P(2, 3)?

For a point located in the second quadrant, which statement about the tangent ratio is true?

Angle α for point Q(-2, 3) is formed with which axis?

What is the measure of angle α given that $ an heta = rac{3}{2}$?

When plotting points in the Cartesian plane, which quadrant is characterized by positive x and negative y coordinates?

Which trigonometric ratio is positive in Quadrant III?

What is the sine value of $45^ heta$?

When the angle θ is $90^ heta$, what is the value of cos θ?

In which quadrant are only the cosine and secant trigonometric ratios positive?

Which of the following statements is true regarding the tangent of $30^ heta$?

Which trigonometric ratio is defined as $\frac{y}{x}$?

If point Q is located at (-2, 3) in the Cartesian plane, what is the general formula to determine angle B formed between line OQ and the positive x-axis?

What is the correct relationship between angle α and angle B when considering point Q(-2, 3) in the Cartesian plane?

When determining the angle θ formed by point P(2, 3) with the x-axis, which of the following represents the radius of the circle centered at the origin?

Which of the following statements correctly describes the coordinates of point P(2, 3) in relation to angle A?

For angle B formed by point Q(-2, 3), which of the following correctly describes the tangent ratio in this case?

What would be the approximate degree measure of angle A formed at point P(2, 3)?

When plotting a point P(x, y) in relation to the radius r, which of the following statements is true?

In dealing with angles in the Cartesian plane, which statement correctly compares angles formed in the first and second quadrants?

In which quadrant is the sine value positive and the tangent value undefined?

Given the angle $45^\circ$, what is the value of cosecant?

Which trigonometric ratio is represented by the formula $\frac{r}{y}$?

What is the tangent value for angle $30^\circ$?

For angles in Quadrant IV, which of the following trigonometric ratios is positive?

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