Q: Which of the following is the correct reciprocal identity for $$\sin \theta$$?

$$\sin \theta = \frac{1}{\csc \theta}$$

Q: Which of the following is a Pythagorean identity?

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

Q: Which of the following is the correct quotient identity for $$\tan \theta$$?

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

Question 1

A surveyor measures an angle of $$37.25^	ext{o} in $$decimal degrees. What is this angle in degrees, minutes, and seconds?

Accepted Answer

$$37^	ext{o}15'0''$$

Question 2

If an angle measures $$112^	ext{o}30'$$, what is its supplement?

Accepted Answer

$$67^	ext{o}30'$$

Question 3

Which of the following is the correct reciprocal identity for $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \frac{1}{\csc 	heta}$$

Question 4

A point $$(-3, 4)$$ lies on the terminal side of an angle $$	heta. $$What is $$\sin 	heta$$?

Accepted Answer

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

Question 5

Given $$	an 	heta = -2$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{2}{\sqrt{5}}$$

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

If $$\cos 	heta = -\frac{3}{5}$$ and $$	heta is in $$the third quadrant, what is $$\sin 	heta$$?

Accepted Answer

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

Question 8

Which quadrant does an angle $$	heta$$ belong to if $$\sin 	heta \u003e 0$$ and $$\cos 	heta \u003c 0$$?

Accepted Answer

Second quadrant

Question 9

What is the complement of $$68^	ext{o}45'$$?

Accepted Answer

$$21^	ext{o}15'$$

Question 10

If $$	an 	heta = \frac{5}{12}$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{5}{13}$$

Question 11

A pilot reports a heading of $$245^	ext{o}. $$What is a positive coterminal angle between $$0^	ext{o}$$ and $$360^	ext{o}$$?

Accepted Answer

$$245^	ext{o}$$

Question 12

Which of the following is the correct quotient identity for $$	an 	heta$$?

Accepted Answer

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

Question 13

If $$\csc 	heta = 2$$ and $$	heta is in $$the fourth quadrant, what is $$\sin 	heta$$?

Accepted Answer

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

Question 14

A clock tower casts a shadow of $$20$$ meters when the angle of elevation of the sun is $$30^	ext{o}. $$What is the height of the tower?

Accepted Answer

$$20 	imes 	an 30^	ext{o}$$

Question 15

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the second quadrant, what is $$\cos 	heta$$?

Accepted Answer

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

Question 16

Which of the following is NOT a trigonometric identity?

Accepted Answer

$$\sin 	heta = \cos 	heta$$

Question 17

A ladder leans against a wall making an angle of $$60^	ext{o}$$ with the ground. If the ladder is $$10$$ meters long, how high up the wall does it reach?

Accepted Answer

$$10 	imes \sin 60^	ext{o}$$

Question 18

If $$\cos 	heta = 0.6$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$0.8$$

Question 19

Which of the following is the correct relationship for the supplement of an angle $$x$$?

Accepted Answer

$$180^	ext{o} - x$$

Question 20

If $$	an 	heta = 3$$ and $$	heta is in $$the third quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{10}}$$

Trigonometry Unit 1: Angles and Trigonometric Functions – Study Guide

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