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

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

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

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

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

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

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

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

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

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

Q: Which of the following is a correct Pythagorean identity involving tangent and secant?

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

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

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

Q: Which of the following is true for all $$\theta$$?

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

Question 1

Which of the following is a correct Pythagorean identity?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Simplify the expression $$\dfrac{1 - \cos^2$ x}{\sin x}.$$

Accepted Answer

$$\sin x$$

Question 4

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

Accepted Answer

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

Question 5

If $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 6

Which of the following is an even-odd identity?

Accepted Answer

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

Question 7

Which cofunction identity is correct?

Accepted Answer

$$\sin \left(\dfrac{\pi}{2} - x \right) = \cos x$$

Question 8

Solve for $$x in$$ $$[0, 2\pi)$$: $$2\sin x = 1.$$

Accepted Answer

$$x = \dfrac{\pi}{6},\; x = \dfrac{5\pi}{6}$$

Question 9

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

Accepted Answer

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

Question 10

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\sin 	heta = 0.6$$ and the ladder is 10 ft long, how high up the wall does the ladder reach?

Accepted Answer

$$6 ft$$

Question 11

Simplify the expression $$	an x \cdot \cot x.$$

Accepted Answer

$$1$$

Question 12

Which of the following is a correct Pythagorean identity involving tangent and secant?

Accepted Answer

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

Question 13

If $$\cos 	heta = -\dfrac{5}{13}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{12}{13}$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is true for all $$	heta$$?

Accepted Answer

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

Question 16

If $$	an 	heta = 3$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

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

Fundamental Trigonometric Identities and Their Applications

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