Gr 10 Math Ch 5: Trigonometric Function
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Questions and Answers

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 $a > 0$?

<p>a + q (D)</p> Signup and view all the answers

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

<p>(90°, 0), (270°, 0) (B)</p> Signup and view all the answers

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

<p>Shifts the graph down by |q| units (C)</p> Signup and view all the answers

What is the period of both sine and cosine functions?

<p>360° (D)</p> Signup and view all the answers

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

<p>[1 - 2, 1 + 2] (B)</p> Signup and view all the answers

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

<p>It becomes the sine graph. (A)</p> Signup and view all the answers

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

<p>$ heta eq 90°, 270°$ within $0° ext{ to } 360°$ (D)</p> Signup and view all the answers

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

<p>It shifts the graph vertically. (C)</p> Signup and view all the answers

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

<p>180° (B)</p> Signup and view all the answers

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

<p>$ heta = 90° ext{ and } 270°$ (A)</p> Signup and view all the answers

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

<p>$q$ (B)</p> Signup and view all the answers

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

<p>The branches become steeper. (A)</p> Signup and view all the answers

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

<p>(0°, q) (A)</p> Signup and view all the answers

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

<p>${ \theta : 0° \leq \theta \leq 360°, \theta \neq 90°, 270° }$ (A)</p> Signup and view all the answers

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

<p>At $90°$ and $270°$. (B)</p> Signup and view all the answers

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

<p>It shifts the graph downwards. (D)</p> Signup and view all the answers

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

<p>It is the distance between two consecutive vertical asymptotes. (B)</p> Signup and view all the answers

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

<p>q (D)</p> Signup and view all the answers

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

<p>(180°, -1) (C)</p> Signup and view all the answers

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

<p>Vertical stretch and reflection about the x-axis (A)</p> Signup and view all the answers

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

<p>Shifts the graph up by $q$ units (B)</p> Signup and view all the answers

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

<p>Vertical compression occurs (B)</p> Signup and view all the answers

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

<p>[1, 3] (A)</p> Signup and view all the answers

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

<p>(0°, 0), (180°, 0), and (360°, 0) (B)</p> Signup and view all the answers

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

<p>The period of the function is 720° (D)</p> Signup and view all the answers

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

<p>a + q (C)</p> Signup and view all the answers

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

<p>[-5, 4] (A)</p> 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?

<p>It becomes twice as high. (A)</p> Signup and view all the answers

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

<p>They occur only at $90°$ and $270°$. (C)</p> Signup and view all the answers

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

<p>The amplitude decreases. (D)</p> Signup and view all the answers

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

<p>The x-intercepts change. (D)</p> Signup and view all the answers

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

<p>It becomes a minimum turning point. (B)</p> Signup and view all the answers

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

<p>[1, 5] (D)</p> 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 $q < 0$?

<p>A vertical shift down with steep branches (C)</p> Signup and view all the answers

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

<p>The function is discontinuous at the asymptotes (A)</p> 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?

<p>The branches become steeper (B)</p> Signup and view all the answers

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

<p>All real numbers except $\theta = 90°$ and $\theta = 270°$ (B)</p> Signup and view all the answers

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

<p>Sine graph can be obtained by shifting the cosine graph right by 90°. (C)</p> Signup and view all the answers

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

<p>The value of $q$ only (A)</p> Signup and view all the answers

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

<p>The steepness increases as the absolute value of $a$ increases. (C)</p> Signup and view all the answers

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

<p>90° and 270° (D)</p> Signup and view all the answers

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

<p>The entire graph is shifted downward by $|q|$ units. (A)</p> Signup and view all the answers

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

<p>It depends on the value of $q$ only. (A)</p> Signup and view all the answers

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

<p>The range is all real numbers. (A)</p> Signup and view all the answers

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