$$(1 + \sin\theta) \sec\theta = \sec\theta + \sin\theta \sec\theta = \sec\theta + \tan\theta$$

Question 1

Given the function $$y = 4 - 5 \cos\left(\frac{x}{2} + \frac{\pi}{2}\right)$$, what is the amplitude of the cosine component?

Accepted Answer

$$5$$

Question 2

For the function $$y = 3 \sin\left(2x - \frac{\pi}{2}\right) - 1$$, what is the period?

Accepted Answer

$$\pi$$

Question 3

Which of the following describes the vertical shift for $$y = 4 - 5 \cos\left(\frac{x}{2} + \frac{\pi}{2}\right)$$?

Accepted Answer

Up 4 units

Question 4

What is the phase shift of $$y = 3 \sin\left(2x - \frac{\pi}{2}\right) - 1$$?

Accepted Answer

$$\frac{\pi}{4}$$ units to the right

Question 5

Express $$\cot 330^\circ as a $$function of its reference angle and find its exact value.

Accepted Answer

$$-\sqrt{3}$$

Question 6

Find the exact value of $$\sin\left(\frac{5\pi}{6}\right)$$ without a calculator.

Accepted Answer

$$\frac{1}{2}$$

Question 7

The terminal side of an angle is given by $$2x - y = 0$$, with $$x \leq 0. $$What is the value of $$	an	heta$$?

Accepted Answer

$$2$$

Question 8

Verify the identity: $$\sin^3$ x + \sin x \cos^2$ x = \sin x. $$Which of the following steps is correct?

Accepted Answer

$$\sin^3$ x + \sin x \cos^2$ x = \sin x (\sin^2$ x + \cos^2$ x) = \sin x \cdot 1 = \sin x$$

Question 9

If $$\sin	heta = -\frac{2}{3}$$ and $$270^\circ \u003c 	heta \u003c 360^\circ$$, what is $$\cos	heta$$?

Accepted Answer

$$\frac{\sqrt{5}}{3}$$

Question 10

Find the exact value of $$\cos 105^\circ$$ without a calculator.

Accepted Answer

$$-\frac{\sqrt{6} + \sqrt{2}}{4}$$

Question 11

Find the exact value of $$\sin 15^\circ$$ without a calculator.

Accepted Answer

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

Question 12

Solve the right triangle if $$A = 35^\circ$$, $$c = 1.00. $$What is the length of side $$a ($$opposite angle $$A$$)?

Accepted Answer

$$0.574$$

Question 13

Solve the right triangle if $$a = 27	ext{ cm}$$, $$c = 28.1	ext{ cm}. $$What is the measure of angle $$A ($$opposite side $$a$$)?

Accepted Answer

$$73.7^\circ$$

Question 14

Which of the following is the correct frequency for $$y = 3 \sin\left(2x - \frac{\pi}{2}\right) - 1$$?

Accepted Answer

$$2$$

Question 15

For the function $$y = 4 - 5 \sec\left(\frac{x}{2} + \frac{\pi}{2}\right)$$, what is the period?

Accepted Answer

Question 16

Which of the following is the correct amplitude for $$y = 3 \csc\left(2x - \frac{\pi}{2}\right) - 1$$?

Accepted Answer

$$3$$

Question 17

If $$\sin	heta = -\frac{2}{3}$$ and $$270^\circ \u003c 	heta \u003c 360^\circ$$, what is $$	an	heta$$?

Accepted Answer

Question 18

Verify the identity: $$(1 + \sin	heta) \sec	heta = 	an	heta + \sec	heta. $$Which of the following is a valid step?

Accepted Answer

$$(1 + \sin	heta) \sec	heta = \sec	heta + \sin	heta \sec	heta = \sec	heta + 	an	heta$$

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