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 the correct sum formula for tangent?

$$\tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$$

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

$$\cot \theta = \frac{1}{\tan \theta}$$

Q: Which of the following is true about $$\tan(-\theta)$$?

$$\tan(-\theta) = -\tan \theta$$

Question 1

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

Accepted Answer

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

Question 2

Given $$\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$$, what is $$\cos(75^\circ)$$ using $$\alpha = 45^\circ$$ and $$\beta = 30^\circ$$?

Accepted Answer

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

Question 3

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos(-	heta)$$

Question 4

If $$	an 	heta = \frac{\sin 	heta}{\cos 	heta}$$, what is $$	an(0)$$?

Accepted Answer

$$0$$

Question 5

Which identity correctly expresses $$\sin(\alpha - \beta)$$?

Accepted Answer

$$\sin \alpha \cos \beta - \cos \alpha \sin \beta$$

Question 6

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\sec 	heta = \frac{5}{4}$$, what is $$\cos 	heta$$?

Accepted Answer

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

Question 7

Which of the following is the correct sum formula for tangent?

Accepted Answer

$$	an(\alpha + \beta) = \frac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$$

Question 8

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

Accepted Answer

$$0.75$$

Question 9

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

Accepted Answer

$$\cot 	heta = \frac{1}{	an 	heta}$$

Question 10

A surveyor measures two angles from a point: $$\alpha = 40^\circ$$ and $$\beta = 25^\circ. $$What is $$\sin(\alpha + \beta)$$?

Accepted Answer

$$\sin 40^\circ \cos 25^\circ + \cos 40^\circ \sin 25^\circ$$

Question 11

Which of the following is true about $$	an(-	heta)$$?

Accepted Answer

$$	an(-	heta) = -	an 	heta$$

Question 12

If $$\sin \alpha = \frac{3}{5}$$ and $$\cos \beta = \frac{5}{13}$$, $$\sin \beta = \frac{12}{13}$$, what is $$\sin(\alpha + \beta)$$?

Accepted Answer

$$\frac{3}{5} \cdot \frac{5}{13} + \frac{4}{5} \cdot \frac{12}{13}$$

Question 13

Which of the following is the correct difference formula for cosine?

Accepted Answer

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

Question 14

A pilot flies north, then turns east. If the northward leg is at $$30^\circ$$ and the eastward leg is at $$60^\circ$$, what is $$\sin(30^\circ + 60^\circ)$$?

Accepted Answer

$$\sin 30^\circ \cos 60^\circ + \cos 30^\circ \sin 60^\circ$$

Question 15

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

Accepted Answer

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

Question 16

If $$	an \alpha = 2$$ and $$	an \beta = 3$$, what is $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{2 + 3}{1 - 2 \cdot 3}$$

Question 17

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

Accepted Answer

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

Question 18

If $$\cos 	heta = -0.6$$, what is $$\sec 	heta$$?

Accepted Answer

$$-1.67$$

Question 19

Which of the following is true about $$\csc(-	heta)$$?

Accepted Answer

$$\csc(-	heta) = -\csc 	heta$$

Analytic Trigonometry: Fundamental Identities and Sum/Difference Formulas

Study Guide - Practice Questions

Study Guide - Flashcards