Q: Which of the following is the correct reciprocal identity for $$\sec(\theta)$$?

$$\sec(\theta) = \frac{1}{\cos(\theta)}$$

Q: Which of the following is the correct Pythagorean identity?

$$\sin^2$(\theta) + \cos^2$(\theta) = 1$$

Q: Which of the following is the correct range for $$\cos(\theta)$$?

$$-1 \leq \cos(\theta) \leq 1$$

Q: Which of the following is the correct double angle formula for $$\tan(2\theta)$$?

$$\frac{2 \tan(\theta)}{1 - \tan^2$(\theta)}$$

Question 1

Given the right triangle shown, if the length of the opposite side is 3, the adjacent side is 4, and the hypotenuse is 5, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 2

On the unit circle, what is the value of $$\cos(	heta)$$ for the point $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}ight)$$?

Accepted Answer

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

Question 3

Which of the following is the correct period for $$	an(\omega 	heta)$$?

Accepted Answer

$$\pi/\omega$$

Question 4

If $$\sin(	heta) = \frac{1}{2}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta in $$radians?

Accepted Answer

$$\frac{\pi}{6}$$

Question 5

Which of the following is the correct reciprocal identity for $$\sec(	heta)$$?

Accepted Answer

$$\sec(	heta) = \frac{1}{\cos(	heta)}$$

Question 6

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the ladder is 10 ft long and the distance from the wall to the base of the ladder is 6 ft, what is $$\cos(	heta)$$?

Accepted Answer

$$\frac{6}{10}$$

Question 7

What is the value of $$\sin(2	heta) if$$ $$\sin(	heta) = \frac{3}{5}$$ and $$\cos(	heta) = \frac{4}{5}$$?

Accepted Answer

$$\frac{12}{25}$$

Question 8

Which of the following is the correct Pythagorean identity?

Accepted Answer

$$\sin^2$(	heta) + \cos^2$(	heta) = 1$$

Question 9

If $$	an(	heta) = \frac{y}{x} on $$the unit circle, what is $$\cot(	heta)$$?

Accepted Answer

$$\frac{x}{y}$$

Question 10

Convert $$150^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{6}$$

Question 11

If $$\sin(\alpha) = \frac{3}{5}$$ and $$\cos(\beta) = \frac{4}{5}$$, what is $$\sin(\alpha + \beta)$$?

Accepted Answer

$$\frac{7}{25}$$

Question 12

Which of the following is the correct range for $$\cos(	heta)$$?

Accepted Answer

$$-1 \leq \cos(	heta) \leq 1$$

Question 13

A Ferris wheel has a radius of 20 meters. If a passenger is at an angle $$	heta = 60^\circ$$ from the horizontal, what is their height above the center?

Accepted Answer

$$20 \sin(60^\circ)$$

Question 14

Which of the following is the correct double angle formula for $$	an(2	heta)$$?

Accepted Answer

$$\frac{2 	an(	heta)}{1 - 	an^2$(	heta)}$$

Question 15

If $$\sin(	heta) = 0.6$$, what is $$\csc(	heta)$$?

Accepted Answer

$$1.67$$

Question 16

Which of the following is the correct law of cosines for a triangle with sides $$a$$, $$b$$, $$c$$ and angle $$\alpha$$ opposite side $$a$$?

Accepted Answer

$$a^2$$ = $$b^2$$ + $$c^2 - 2bc$$ \cos(\alpha)$$

Question 17

If $$\sin(	heta) = 0.8$$ and $$\cos(	heta) = 0.6$$, what is $$	an(	heta)$$?

Accepted Answer

$$1.33$$

Question 18

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

Accepted Answer

$$\sin(\alpha + \beta) = \sin(\alpha) \cos(\beta) + \cos(\alpha) \sin(\beta)$$

Question 19

If $$	heta = 45^\circ$$, what are the coordinates on the unit circle?

Accepted Answer

$$\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$$

Comprehensive Trigonometry Reference for Precalculus

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