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

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

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

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

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

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

Q: Which of the following is the correct negative-angle identity for $$\cos(-\theta)$$?

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

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

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

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

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

Q: Which of the following is the correct negative-angle identity for $$\tan(-\theta)$$?

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

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

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

Question 1

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

Accepted Answer

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

Question 2

Given $$	an 	heta = 2.6$$, what is $$	an(-	heta)$$?

Accepted Answer

$$-2.6$$

Question 3

If $$\sin 	heta = \dfrac{2}{3}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{\sqrt{5}}{3}$$

Question 4

Which of the following is the correct Pythagorean identity?

Accepted Answer

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

Question 5

Simplify $$	an 	heta \cos 	heta \csc 	heta$$ using fundamental identities.

Accepted Answer

$$1$$

Question 6

If $$\sec 	heta = \dfrac{11}{4}$$ and $$	an 	heta \u003c 0$$, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{4}{11}$$

Question 7

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

Accepted Answer

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

Question 8

If $$	an 	heta = -\dfrac{1}{4}$$ and $$\cos 	heta \u003e 0$$, in which quadrant is $$	heta$$?

Accepted Answer

Quadrant IV

Question 9

Simplify $$\sin^2$ 	heta (\csc^2$ 	heta - 1).$$

Accepted Answer

$$\cos^2$ 	heta$$

Question 10

Which of the following is the correct negative-angle identity for $$\cos(-	heta)$$?

Accepted Answer

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

Question 11

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

Accepted Answer

$$1.67$$

Question 12

Given $$\sin 	heta = \dfrac{2}{3}$$ and $$	heta is in $$Quadrant II, what is $$	an 	heta$$?

Accepted Answer

$$-\dfrac{2}{\sqrt{5}}$$

Question 13

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

Accepted Answer

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

Question 14

Simplify $$\dfrac{\cos^2$ 	heta - \sin^2$ 	heta}{\sin 	heta \cos 	heta}.$$

Accepted Answer

$$\cot 	heta - 	an 	heta$$

Question 15

If $$\sin 	heta = \dfrac{2}{3}$$ and $$	heta is in $$Quadrant II, what is $$\sec 	heta$$?

Accepted Answer

$$-\dfrac{3}{\sqrt{5}}$$

Question 16

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

Accepted Answer

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

Question 17

If $$	an 	heta = 1.6$$, what is $$\cot 	heta$$?

Accepted Answer

$$0.625$$

Question 18

Which of the following is the correct negative-angle identity for $$	an(-	heta)$$?

Accepted Answer

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

Question 19

A Ferris wheel rotates such that the height $$h (in $$meters) above the ground of a seat is modeled by $$h = 10 + 8 \sin 	heta. If$$ $$\sin 	heta = 0.5$$, what is the height of the seat?

Accepted Answer

$$14$$ meters

Question 20

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

Accepted Answer

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

Trigonometric Identities: Fundamental, Reciprocal, Quotient, Pythagorean, and Negative-Angle Identities

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