4. which statements are true for both functions y = cos(θ) and y = sin(θ)? select all that apply. a. the…

4. which statements are true for both functions y = cos(θ) and y = sin(θ)? select all that apply. a. the function is periodic. b. the maximum value is 1. c. the maximum value occurs at θ = 0. d. the period of the function is 2π. e. the function has a value of about 0.71 when θ = π/4. f. the function has a value of about 0.71 when θ = 3π/4.

4. which statements are true for both functions y = cos(θ) and y = sin(θ)? select all that apply. a. the function is periodic. b. the maximum value is 1. c. the maximum value occurs at θ = 0. d. the period of the function is 2π. e. the function has a value of about 0.71 when θ = π/4. f. the function has a value of about 0.71 when θ = 3π/4.

Answer

Explanation:

Step1: Recall properties of sine and cosine

Both (y = \sin(\theta)) and (y=\cos(\theta)) are periodic functions.

Step2: Determine period

The period of both (y = \sin(\theta)) and (y=\cos(\theta)) is (2\pi).

Step3: Find maximum value

The range of both (y = \sin(\theta)) and (y=\cos(\theta)) is ([- 1,1]), so the maximum value is 1.

Step4: Evaluate at (\theta=\frac{\pi}{4})

(\sin(\frac{\pi}{4})=\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\approx0.71).

Step5: Evaluate at (\theta = \frac{3\pi}{4})

(\sin(\frac{3\pi}{4})=\frac{\sqrt{2}}{2}\approx0.71) and (\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}\approx - 0.71).

Step6: Check maximum - value location

For (y = \cos(\theta)), the maximum occurs at (\theta = 2k\pi,k\in\mathbb{Z}), for (y=\sin(\theta)), the maximum occurs at (\theta=\frac{\pi}{2}+2k\pi,k\in\mathbb{Z}), so the maximum does not occur at (\theta = 0) for both.

Answer:

A. The function is periodic. B. The maximum value is 1. D. The period of the function is (2\pi). E. The function has a value of about 0.71 when (\theta=\frac{\pi}{4}).