Gr 11 Math Ch 5: The Cosine Function

Play an AI-generated podcast conversation about this lesson

What is the period of the function y = cos θ?

180°

90°

720°

360° (correct)

What is the amplitude of the function y = 2cos θ?

-1

0.5

2 (correct)

1

What is the effect of q > 0 on the graph of y = acos θ + q?

The graph shifts vertically downwards by q units.

The graph shifts horizontally to the right by q units.

The graph shifts vertically upwards by q units. (correct)

The graph shifts horizontally to the left by q units.

What is the period of the function y = cos 2θ?

180° Signup and view all the answers

What is the y-intercept of the function y = cos θ?

(0°, 1) Signup and view all the answers

What is the effect of a < 0 on the graph of y = acos θ?

The graph is reflected about the x-axis. Signup and view all the answers

What is the range of the function y = cos kθ?

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

What is the x-intercept of the function y = cos θ?

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

What is the effect of a > 1 on the graph of y = a cos θ?

The amplitude increases. Signup and view all the answers

What is the period of the function y = cos 3θ?

120° Signup and view all the answers

What is the x-intercept of the function y = cos 2θ?

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

What is the effect of q < 0 on the graph of y = a cos θ + q?

The graph shifts vertically downwards by q units. Signup and view all the answers

What is the domain of the function y = cos kθ?

{θ : θ ∈ ℝ} Signup and view all the answers

What is the y-intercept of the function y = cos kθ?

(0°, 1) Signup and view all the answers

What is the effect of k < -1 on the period of the function y = cos kθ?

The period decreases. Signup and view all the answers

What is the effect of -1 < a < 0 on the graph of y = a cos θ?

The amplitude of the function decreases with reflection. Signup and view all the answers

What is the period of the function y = cos(2/3)θ?

540°/3 Signup and view all the answers

What is the effect of a = -2 on the graph of y = a cos θ?

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

What is the x-intercept of the function y = cos(θ/2) + 1?

There are no x-intercepts. Signup and view all the answers

What is the maximum turning point of the function y = 2cos θ?

(0°, 2) Signup and view all the answers

What is the effect of k = -3 on the period of the function y = cos kθ?

The period increases. Signup and view all the answers

What is the y-intercept of the function y = cos(θ/4) + 2?

(0°, 3) Signup and view all the answers

What is the effect of q = 2 on the graph of y = a cos θ + q?

The graph shifts vertically upwards by 2 units. Signup and view all the answers

What is the range of the function y = 3cos(2θ) + 1?

[-3, 3] Signup and view all the answers

What is the effect of $k > 1$ on the period of the function $y = \cos k heta$?

The period decreases. Signup and view all the answers

What is the effect of $a < -1$ on the graph of $y = a \cos heta$?

The amplitude increases with reflection. Signup and view all the answers

What is the x-intercept of the function $y = \cos heta + 2$?

There is no x-intercept. Signup and view all the answers

What is the maximum turning point of the function $y = \cos 2 heta$?

(45, 1) Signup and view all the answers

What is the effect of $q < 0$ on the graph of $y = a \cos heta + q$?