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

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

Q: Using the complementary angle theorem, which of the following is true?

$$\sin(90^\circ - \theta) = \cos \theta$$

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

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

Question 1

A right triangle has legs of length 3 and 4. What is the value of $$\sin 	heta$$ where $$	heta is $$the angle opposite the side of length 3?

Accepted Answer

$$\dfrac{3}{5}$$

Question 2

Which of the following is a correct statement of the Pythagorean identity?

Accepted Answer

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

Question 3

Given $$\sin 	heta = \dfrac{2}{5}$$ and $$	heta is an $$acute angle, what is $$\cos 	heta$$?

Accepted Answer

$$\dfrac{\sqrt{21}}{5}$$

Question 4

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

Accepted Answer

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

Question 5

A meteorologist uses a clinometer to measure the angle of elevation to a cloud as $$75^\circ$$ from a point 300 ft from the base of the building. If the building is 400 ft tall, what is the height of the cloud above the ground? (Round your answer to the nearest foot.)

Accepted Answer

$$1120 ft$$

Question 6

If $$	an 	heta = \dfrac{3}{4}$$ and $$	heta is an $$acute angle, what is $$\sin 	heta$$?

Accepted Answer

$$\dfrac{3}{5}$$

Question 7

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

Accepted Answer

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

Question 8

Using the complementary angle theorem, which of the following is true?

Accepted Answer

$$\sin(90^\circ - 	heta) = \cos 	heta$$

Question 9

Find the exact value of $$\sin 45^\circ.$$

Accepted Answer

$$\dfrac{\sqrt{2}}{2}$$

Question 10

Given $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is an $$acute angle, what is $$	an 	heta$$?

Accepted Answer

$$\dfrac{3}{4}$$

Question 11

Which of the following is the correct value for $$\cos 60^\circ$$?

Accepted Answer

$$\dfrac{1}{2}$$

Question 12

If $$\sin 	heta = \dfrac{5}{13}$$ and $$	heta is an $$acute angle, what is $$\sec 	heta$$?

Accepted Answer

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

Question 13

Which of the following is the correct value for $$	an 30^\circ$$?

Accepted Answer

$$\dfrac{1}{\sqrt{3}}$$

Question 14

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the foot of the ladder is 5 ft from the wall, how long is the ladder?

Accepted Answer

$$10 ft$$

Question 15

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

Accepted Answer

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

Question 16

If $$\cos 	heta = \dfrac{4}{5}$$ and $$	heta is an $$acute angle, what is $$\cot 	heta$$?

Accepted Answer

$$2$$

Question 17

Find the exact value of $$\sec 45^\circ.$$

Accepted Answer

$$\sqrt{2}$$

Question 18

Which of the following is the correct value for $$\sin 60^\circ$$?

Accepted Answer

$$\dfrac{\sqrt{3}}{2}$$

Question 19

Given $$\sin 	heta = \dfrac{4}{5}$$ and $$	heta is an $$acute angle, what is $$\csc 	heta$$?

Accepted Answer

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

Right Triangle Trigonometry and Trigonometric Functions of Acute Angles

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