Gr 10 Math Ch 5: Trigonometric Function

What is the range of the sine function $y = ext{sin} \theta$?

[-1, 1] (correct)

[-2, 2]

[0, 360]

[0, 1]

Which point is a maximum turning point of the sine function $y = ext{sin} \theta$?

(0°, 0)

(270°, -1)

(90°, 1) (correct)

(180°, 0)

If $a < 0$ in the function $y = a ext{sin} \theta + q$, what transformation occurs?

Reflection about the x-axis (correct)

Vertical shift up

Vertical compression

Horizontal shift to the right

For the cosine function $y = a ext{cos} \theta + q$, what is the y-intercept when $a > 0$?

a + q Signup and view all the answers

What are the x-intercepts of the cosine function $y = ext{cos} \theta$?

(90°, 0), (270°, 0) Signup and view all the answers

Which statement correctly describes the effect of $q$ when $q < 0$ in $y = a ext{sin} \theta + q$?

Shifts the graph down by |q| units Signup and view all the answers

What is the period of both sine and cosine functions?

360° Signup and view all the answers

What happens to the range of the sine function when $a = 2$ and $q = 1$?

[1 - 2, 1 + 2] Signup and view all the answers

What occurs to the cosine graph when it is shifted to the right by 90°?

It becomes the sine graph. Signup and view all the answers

What is the domain of the tangent function defined as $y = an heta$?

$ heta eq 90°, 270°$ within $0° ext{ to } 360°$ Signup and view all the answers

What effect does changing the value of $q$ have in the function $y = a an heta + q$?

It shifts the graph vertically. Signup and view all the answers

What is the period of the tangent function $y = an heta$?

180° Signup and view all the answers

Where are the asymptotes located for the tangent function graph within the defined domain?

$ heta = 90° ext{ and } 270°$ Signup and view all the answers

What is the y-intercept of the function $y = a an heta + q$?

$q$ Signup and view all the answers

What happens to the steepness of the branches in the tangent function when the value of $a$ increases?

The branches become steeper. Signup and view all the answers

Which of the following is the correct y-intercept for the function $y = a \tan \theta + q$?

(0°, q) Signup and view all the answers

What is the domain of the tangent function $y = \tan \theta$?

${ \theta : 0° \leq \theta \leq 360°, \theta \neq 90°, 270° }$ Signup and view all the answers

At what angles do the asymptotes of the tangent function occur?

At $90°$ and $270°$. Signup and view all the answers

What is the effect of a negative value of $q$ in the function $y = a \tan \theta + q$?

It shifts the graph downwards. Signup and view all the answers

What is the significance of the period in the tangent function $y = \tan \theta$?

It is the distance between two consecutive vertical asymptotes. Signup and view all the answers

What is the y-intercept of the sine function of the form $y = a \sin \theta + q$ when $a > 0$?

q Signup and view all the answers

Which point is a minimum turning point of the cosine function $y = \cos \theta$?

(180°, -1) Signup and view all the answers

If $a = -2$ in the function $y = a \sin \theta + q$, what transformation occurs to the graph?

Vertical stretch and reflection about the x-axis Signup and view all the answers

What effect does a positive value of $q$ have on the sine function $y = a \sin \theta + q$?

Shifts the graph up by $q$ units Signup and view all the answers

For the function $y = a \cos \theta + q$ with $0 < |a| < 1$, what happens to the graph?

Vertical compression occurs Signup and view all the answers

Which of the following best describes the range of the sine function $y = 2 \sin \theta + 1$?

[1, 3] Signup and view all the answers

What are the x-intercepts of the sine function $y = \sin \theta$?

(0°, 0), (180°, 0), and (360°, 0) Signup and view all the answers

If the cosine function is represented as $y = \cos \theta$, which of the following statements is false?

The period of the function is 720° Signup and view all the answers

What is the y-intercept of the cosine function of the form $y = a \cos \theta + q$ when $a < 0$?

a + q Signup and view all the answers

Which range is correct for the transformed sine function $y = 3 \sin \theta - 2$?

[-5, 4] Signup and view all the answers

If the amplitude of a sine function is doubled while keeping the vertical shift constant, what happens to the maximum turning point?

It becomes twice as high. Signup and view all the answers

Which statement is true regarding the cosine function's x-intercepts?

They occur only at $90°$ and $270°$. Signup and view all the answers

What is the effect on the sine function $y = a \sin \theta + q$ if $|a| < 1$?

The amplitude decreases. Signup and view all the answers

Which transformation occurs when the sine function $y = \sin \theta$ is shifted left by $90°$?

The x-intercepts change. Signup and view all the answers

How does the cosine function's maximum turning point change if the amplitude $a$ is negative?

It becomes a minimum turning point. Signup and view all the answers

Which of the following intervals defines the range of the transformed function $y = -2 \sin \theta + 3$?

[1, 5] Signup and view all the answers

What is the shape of the graph for the tangent function defined as $y = a \tan \theta + q$ when $a > 0$ and $q < 0$?

A vertical shift down with steep branches Signup and view all the answers

Which of the following describes the behavior of the tangent function $y = \tan \theta$ at its asymptotes?

The function is discontinuous at the asymptotes Signup and view all the answers

If the value of $a$ in the function $y = a \tan \theta + q$ is increased to a large positive value, what effect does it have on the graph's branches?

The branches become steeper Signup and view all the answers

Which statement correctly describes the domain of the function $y = a \tan \theta + q$?

All real numbers except $\theta = 90°$ and $\theta = 270°$ Signup and view all the answers

Which of the following statements is true about the relationship between the sine and cosine graphs?

Sine graph can be obtained by shifting the cosine graph right by 90°. Signup and view all the answers

What determines the position of the y-intercept for the function $y = a \tan \theta + q$?

The value of $q$ only Signup and view all the answers

Which statement about the tangent function $y = a an \theta + q$ is correct regarding its steepness?

The steepness increases as the absolute value of $a$ increases. Signup and view all the answers

At which specific angles does the tangent function $y = an \theta$ exhibit its vertical asymptotes?

90° and 270° Signup and view all the answers

What transformation occurs to the tangent function $y = a an \theta + q$ when $q < 0$?

The entire graph is shifted downward by $|q|$ units. Signup and view all the answers

Which of the following correctly identifies the y-intercept for the tangent function $y = a an \theta + q$?

It depends on the value of $q$ only. Signup and view all the answers

What is the range of the tangent function $y = an \theta$ within the defined domain?

The range is all real numbers. Signup and view all the answers