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

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

Q: Which of the following is a Pythagorean identity?

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

Q: Which of the following expresses the cotangent in terms of sine and cosine?

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

Q: Which of the following is the correct complementary angle identity?

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

Q: Which of the following is the correct quotient identity for tangent?

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

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

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

Question 1

Given a right triangle with sides $$a = 5$$, $$b = 12$$, and $$c = 13$$, what is the value of $$\sin 	heta if$$ $$	heta is $$the angle opposite the side of length $$b$$?

Accepted Answer

$$\frac{12}{13}$$

Question 2

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

Accepted Answer

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

Question 3

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is an $$acute angle, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 4

Given $$	an 	heta = \frac{2}{3}$$ and $$	heta is $$acute, what is $$\sin 	heta$$?

Accepted Answer

Question 5

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is $$acute, what is $$\cot 	heta$$?

Accepted Answer

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

If $$\sin 	heta = \frac{4}{5}$$ and $$	heta is $$acute, what is $$\sec 	heta$$?

Accepted Answer

Question 8

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the ladder is 10 ft long and the base is 6 ft from the wall, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{6}{10}$$

Question 9

Which of the following expresses the cotangent in terms of sine and cosine?

Accepted Answer

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

Question 10

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is $$acute, what is $$\csc 	heta$$?

Accepted Answer

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

Question 11

If $$\cos 	heta = \frac{5}{13}$$ and $$	heta is $$acute, what is $$	an 	heta$$?

Accepted Answer

$$\frac{12}{5}$$

Question 12

Which of the following is the correct complementary angle identity?

Accepted Answer

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

Question 13

A ramp rises 4 ft over a horizontal distance of 7 ft. What is $$	an 	heta$$ where $$	heta is $$the angle the ramp makes with the ground?

Accepted Answer

$$\frac{4}{7}$$

Question 14

If $$\sin 	heta = \frac{5}{13}$$ and $$	heta is $$acute, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 15

Which of the following is the correct quotient identity for tangent?

Accepted Answer

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

Question 16

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is $$acute, what is $$	an 	heta$$?

Accepted Answer

$$\frac{3}{4}$$

Question 17

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is $$acute, what is $$\sec 	heta$$?

Accepted Answer

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

$$\frac{4}{5}$$

Right Triangle Trigonometry: Trigonometric Functions of Acute Angles

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