Gr 11 Math Ch 5: The Sine Function
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Gr 11 Math Ch 5: The Sine Function

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@GreatestTiger

Questions and Answers

What is the period of the function y = sinθ?

360°

What is the amplitude of the function y = 2sinθ?

2

What is the effect of q on the function y = sinθ + q?

Vertical shift

What is the x-intercept of the function y = sinθ?

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

What is the period of the function y = sinkθ?

<p>360°/|k|</p> Signup and view all the answers

What is the effect of k on the function y = sinkθ if k is negative?

<p>Reflection about the y-axis</p> Signup and view all the answers

What is the effect of p on the function y = sin(θ + p)?

<p>Horizontal shift</p> Signup and view all the answers

What is the domain of the function y = sinkθ?

<p>{θ : θ ∈ ℝ}</p> Signup and view all the answers

What is the range of the function y = sinθ?

<p>[-1, 1]</p> Signup and view all the answers

What is the effect of a in the function y = a sinθ when a > 1?

<p>The amplitude increases.</p> Signup and view all the answers

What is the effect of k in the function y = sin kθ when k < 0?

<p>The graph is reflected about the y-axis.</p> Signup and view all the answers

What is the x-intercept of the function y = sinθ?

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

What is the maximum turning point of the function y = sinθ?

<p>(90, 1)</p> Signup and view all the answers

What is the effect of p in the function y = sin(θ + p) when p > 0?

<p>The graph shifts to the left by p units.</p> Signup and view all the answers

What is the y-intercept of the function y = sinθ?

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

What is the domain of the function y = sinθ?

<p>[0, ∞)</p> Signup and view all the answers

What is the effect of q on the graph of y = a sinθ + q if a is negative?

<p>The graph shifts vertically downwards by q units and is reflected about the x-axis.</p> Signup and view all the answers

What is the period of the function y = sin(2θ)?

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

What is the effect of a on the graph of y = a sinθ if a = -0.5?

<p>The graph is reflected about the x-axis and the amplitude is decreased.</p> Signup and view all the answers

What is the effect of k on the graph of y = sin(kθ) if k = -2?

<p>The graph is reflected about the y-axis and the period is halved.</p> Signup and view all the answers

What is the x-intercept of the function y = sin(θ + 30°)?

<p>(-30°, 0)</p> Signup and view all the answers

What is the y-intercept of the function y = 2sinθ + 1?

<p>(0°, 1)</p> Signup and view all the answers

What is the maximum turning point of the function y = -sinθ?

<p>(270°, -1)</p> Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p) if p = -60°?

<p>The graph shifts to the right by 60°.</p> Signup and view all the answers

What is the period of the function y = sin(3θ)?

<p>60°</p> Signup and view all the answers

What is the amplitude of the function y = -2sin(θ + 30°)?

<p>4</p> Signup and view all the answers

What is the minimum turning point of the function y = sin(θ - 45°)?

<p>(270°, -1)</p> Signup and view all the answers

What is the effect of a on the function y = a sin(θ) + 2 when a = -3?

<p>The graph is reflected about the x-axis and the amplitude increases.</p> Signup and view all the answers

What is the x-intercept of the function y = sin(2θ + 30°)?

<p>(15°, 0)</p> Signup and view all the answers

What is the effect of p on the function y = sin(θ + p) when p = 90°?

<p>The graph shifts to the left by 90°.</p> Signup and view all the answers

What is the maximum turning point of the function y = -sin(2θ)?

<p>(90°, -1)</p> Signup and view all the answers

What is the range of the function y = 2sin(θ) + 1?

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

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