$$\frac{\tan\alpha + \tan\beta}{1 - \tan\alpha \tan\beta}$$

Question 1

Given the function $$y = 2 \sin(x)$$, what is the amplitude and period of the function?

Accepted Answer

Amplitude: 2, Period: $$2\pi$$

Question 2

For the function $$g(x) = -2 \cos(x - \pi)$$, what is the phase shift?

Accepted Answer

$$\pi$$ units to the right

Question 3

Which of the following is the correct value for $$\sin(0)$$?

Accepted Answer

$$0$$

Question 4

If $$	an(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$$, what is $$	an(60^\circ)$$?

Accepted Answer

$$\sqrt{3}$$

Question 5

Which identity is used to simplify $$\sin(\alpha + \beta)$$?

Accepted Answer

$$\sin\alpha \cos\beta + \cos\alpha \sin\beta$$

Question 6

Evaluate $$\cos(285^\circ)$$ using the sum or difference identity.

Accepted Answer

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

Question 7

If $$\sin(	heta) \u003c 0$$ and $$	an(	heta) \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 8

Which of the following is equivalent to $$\cos^2$(x) + \sin^2$(x)$$?

Accepted Answer

$$1$$

Question 9

Given $$\sin(\alpha) = \frac{3}{5}$$ and $$\alpha is in $$Quadrant II, what is $$\cos(\alpha)$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 10

Which of the following is the correct double angle formula for $$\sin(2x)$$?

Accepted Answer

$$2\sin(x)\cos(x)$$

Question 11

If $$	an(x) = 1$$, what is the value of $$x in $$the interval $$[0, 2\pi)$$?

Accepted Answer

$$\frac{\pi}{4}$$ and $$\frac{5\pi}{4}$$

Question 12

Which of the following is the correct value for $$\sin(\pi)$$?

Accepted Answer

$$0$$

Question 13

If $$\cos(	heta) = -\frac{1}{2}$$ and $$	heta is in $$Quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 14

Which of the following is the correct formula for $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{	an\alpha + 	an\beta}{1 - 	an\alpha 	an\beta}$$

Question 15

Evaluate $$\sin(\frac{5\pi}{6}).$$

Accepted Answer

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

Question 16

If $$\sin(\alpha) = \frac{5}{13}$$ and $$\alpha is in $$Quadrant II, what is $$\cos(\alpha)$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 17

Which of the following is the correct value for $$\cos(0)$$?

Accepted Answer

$$1$$

Question 18

If $$	an(	heta) = -1$$ and $$	heta is in $$Quadrant IV, what is $$	heta$$?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 19

Which of the following is the correct value for $$\cos(\pi)$$?

Accepted Answer

$$-1$$

Trigonometry Exam 3 Study Guide Solutions

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