Q: Which trigonometric identity is used to verify $$(1 + \sin \theta) \sec \theta = \tan \theta + \sec \theta$$?

$$\tan \theta = \frac{\sin \theta}{\cos \theta}$$

Question 1

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

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

Accepted Answer

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

Question 4

What is the exact value of $$\cot 330^\circ$$?

Accepted Answer

$$\sqrt{3}$$

Question 5

Find the exact value of $$\sin\left(\frac{5\pi}{6}\right).$$

Accepted Answer

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

Question 6

Given the equation $$2x - y = 0$$ with $$x \leq 0$$, what is $$	an 	heta$$ for the angle whose terminal side lies on this line?

Accepted Answer

$$-2$$

Question 7

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

Accepted Answer

Factor $$\sin x to $$get $$\sin x (\sin^2$ x + \cos^2$ x)$$

Question 8

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 9

Find the exact value of $$\cos 105^\circ.$$

Accepted Answer

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

Question 10

Find the exact value of $$\sin 15^\circ.$$

Accepted Answer

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

Question 11

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

Accepted Answer

$$0.574$$

Question 12

Solve for $$b in a $$right triangle where $$a = 27 cm $$and $$c = 28.1 cm.$$

Accepted Answer

$$b = 8.1 cm$$

Question 13

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

Accepted Answer

$$4$$ units up

Question 14

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

Accepted Answer

$$2$$

Question 15

Which trigonometric identity is used to verify $$(1 + \sin 	heta) \sec 	heta = 	an 	heta + \sec 	heta$$?

Accepted Answer

$$	an 	heta = \frac{\sin 	heta}{\cos 	heta}$$

Question 16

Which of the following best describes the graph of $$y = 4 - 5 \sec\left(\frac{x}{2} + \frac{\pi}{2}\right)$$ compared to $$y = 4 - 5 \cos\left(\frac{x}{2} + \frac{\pi}{2}\right)$$?

Accepted Answer

It has the same period and phase shift, but vertical asymptotes where the cosine is zero.

Question 17

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

Accepted Answer

Question 18

Which of the following is the correct reference angle for $$330^\circ$$?

Accepted Answer

$$30^\circ$$

Question 19

If $$y = 3 \csc\left(2x - \frac{\pi}{2}\right) - 1$$, what is the range of the function?

Accepted Answer

$$(-\infty, -1 - 3] \cup [-1 + 3, \infty)$$

Precalculus Trigonometry Test 2 – Step-by-Step Study Guidance

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