Q: Which of the following is the correct definition of $$\tan \theta in $$terms of the sides of a right triangle?

$$\tan \theta = \dfrac{\text{opp}}{\text{adj}}$$

Q: Which of the following is a Pythagorean identity?

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

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

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

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

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

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

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

Q: A ramp rises 3 ft vertically and is 12 ft long. What is the sine of the angle the ramp makes with the ground?

$$\sin \theta = \dfrac{3}{12} = \dfrac{1}{4}$$

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

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

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

$$\tan \theta = \cot \left( \dfrac{\pi}{2} - \theta \right)$$

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

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

Question 1

Which of the following is the correct definition of $$	an 	heta in $$terms of the sides of a right triangle?

Accepted Answer

$$	an 	heta = \dfrac{	ext{opp}}{	ext{adj}}$$

Question 2

Simplify $$\dfrac{1}{\sqrt{24}}$$ and rationalize the denominator.

Accepted Answer

$$\dfrac{\sqrt{6}}{12}$$

Question 3

Given a $$45^\	ext{o}$$-$$45^\	ext{o}$$-$$90^\	ext{o}$$ triangle with legs of length 1, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{2}$$

Question 4

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 5

If $$\sin 	heta = \dfrac{1}{2}$$ and $$	heta is an $$acute angle, what is $$	heta$$?

Accepted Answer

$$30^\circ$$

Question 6

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

Accepted Answer

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

Question 7

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach?

Accepted Answer

$$10 \sin 60^\circ = 5 \sqrt{3} ft$$

Question 8

Simplify $$\dfrac{\sqrt{50}}{\sqrt{2}}.$$

Accepted Answer

$$5$$

Question 9

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

Accepted Answer

$$\sin 	heta = \cos \left( \dfrac{\pi}{2} - 	heta ight)$$

Question 10

If $$	an 	heta = 1$$, what is $$	heta in $$degrees, assuming $$	heta is $$acute?

Accepted Answer

$$45^\circ$$

Question 11

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

Accepted Answer

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

Question 12

A ramp rises 3 ft vertically and is 12 ft long. What is the sine of the angle the ramp makes with the ground?

Accepted Answer

$$\sin 	heta = \dfrac{3}{12} = \dfrac{1}{4}$$

Question 13

Simplify $$\dfrac{1}{\sqrt{63}}$$ and rationalize the denominator.

Accepted Answer

$$\dfrac{\sqrt{7}}{21}$$

Question 14

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

Accepted Answer

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

Question 15

If $$\cos 	heta = \dfrac{1}{2}$$ and $$	heta is an $$acute angle, what is $$	heta$$?

Accepted Answer

$$60^\circ$$

Question 16

Which of the following is the correct simplified form of $$\dfrac{\sqrt{18}}{\sqrt{2}}$$?

Accepted Answer

$$3$$

Question 17

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

Accepted Answer

$$	an 	heta = \cot \left( \dfrac{\pi}{2} - 	heta ight)$$

Question 18

A triangle has sides of length 1, $$\sqrt{3}$$, and 2. What is the measure of the smallest angle?

Accepted Answer

$$30^\circ$$

Question 19

Which of the following is the correct Pythagorean identity involving $$	an 	heta$$ and $$\sec 	heta$$?

Accepted Answer

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

Right Triangle Trigonometry and Simplifying Radical Expressions

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