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

$$\tan^2$ \theta + 1 = \sec^2$ \theta$$

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

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

Q: Which of the following expresses $$\tan \theta in $$terms of $$\sin \theta$$ and $$\cos \theta$$?

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

Q: Which of the following is an even-odd identity?

$$\sin(-\theta) = -\sin \theta$$

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

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

Q: Which of the following is a reciprocal identity?

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

Q: Which of the following is the correct Pythagorean identity involving $$\cot \theta$$ and $$\csc \theta$$?

$$1 + \cot^2$ \theta = \csc^2$ \theta$$

Q: Which of the following is the correct even-odd identity for $$\cos \theta$$?

$$\cos(-\theta) = \cos \theta$$

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

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

Question 1

Which of the following is a correct Pythagorean identity?

Accepted Answer

$$	an^2$ 	heta + 1 = \sec^2$ 	heta$$

Question 2

If $$	an 	heta = -\frac{5}{3}$$ and $$	heta is in $$quadrant II, what is $$\sec 	heta$$?

Accepted Answer

$$-\frac{\sqrt{34}}{3}$$

Question 3

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

Accepted Answer

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

Question 4

Given $$	an \alpha = -\frac{1}{4}$$ and $$\alpha is in $$quadrant IV, what is $$\cot \alpha$$?

Accepted Answer

$$4$$

Question 5

Which of the following expresses $$	an 	heta in $$terms of $$\sin 	heta$$ and $$\cos 	heta$$?

Accepted Answer

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

Question 6

If $$	an 	heta = -\frac{5}{3}$$ and $$	heta is in $$quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{5\sqrt{34}}{34}$$

Question 7

Which of the following is an even-odd identity?

Accepted Answer

$$\sin(-	heta) = -\sin 	heta$$

Question 8

Simplify $$\sec^2$(-	heta) - \cos^2$(-	heta) - 	an^2$(-	heta) in $$terms of $$\sin 	heta$$ and $$\cos 	heta.$$

Accepted Answer

$$1$$

Question 9

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

Accepted Answer

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

Question 10

If $$	an 	heta = -\frac{5}{3}$$ and $$	heta is in $$quadrant II, what is $$\cot(-	heta)$$?

Accepted Answer

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

Question 11

Which of the following is a reciprocal identity?

Accepted Answer

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

Question 12

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\sin 	heta = 0.6$$, what is $$\cos 	heta if$$ $$	heta is in $$quadrant I?

Accepted Answer

$$0.8$$

Question 13

Which of the following is the correct Pythagorean identity involving $$\cot 	heta$$ and $$\csc 	heta$$?

Accepted Answer

$$1 + \cot^2$ 	heta = \csc^2$ 	heta$$

Question 14

If $$	an 	heta = -\frac{5}{3}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{34}}$$

Question 15

Which of the following is the correct even-odd identity for $$\cos 	heta$$?

Accepted Answer

$$\cos(-	heta) = \cos 	heta$$

Question 16

A Ferris wheel rotates such that the height $$h$$ above the ground of a seat is modeled by $$h = 10 + 8\sin 	heta. $$What is the maximum height the seat reaches?

Accepted Answer

$$18$$

Question 17

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

Accepted Answer

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

Question 18

If $$	an 	heta = -\frac{5}{3}$$ and $$	heta is in $$quadrant II, what is $$\csc 	heta$$?

Accepted Answer

$$\frac{\sqrt{34}}{5}$$

Chapter 7: Fundamental Trigonometric Identities and Their Applications

Study Guide - Practice Questions

Study Guide - Flashcards