Q: Given a right triangle with sides $$a = 5$$, $$b = 12$$, and hypotenuse $$c = 13$$, what is the value of $$\sin \theta$$ where $$\theta is $$the angle adjacent to side $$a$$?

$$\sin \theta = \dfrac{12}{13}$$

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

$$\tan \theta = \dfrac{1}{\cot \theta}$$

Q: Given $$\tan \theta = \dfrac{2}{3}$$ and $$\theta is $$acute, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{2}{\sqrt{13}}$$

Q: If $$\sin \theta = \dfrac{1}{2}$$ and $$\theta is $$acute, what is $$\sec \theta$$?

$$\sec \theta = \dfrac{2}{\sqrt{1 - (1/2)^2$}}$$

Q: Which of the following is a Pythagorean identity?

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

Q: A ladder leans against a wall making an angle $$\theta$$ with the ground. If the foot of the ladder is $$6 ft $$from the wall and the ladder is $$10 ft $$long, what is $$\cos \theta$$?

$$\cos \theta = \dfrac{6}{10}$$

Q: If $$\sin \theta = \dfrac{5}{13}$$ and $$\theta is $$acute, what is $$\csc \theta$$?

$$\csc \theta = \dfrac{13}{5}$$

Q: Which of the following expresses the Complementary Angle Theorem?

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

Q: If $$\tan \theta = 7$$ and $$\theta is $$acute, what is $$\sec \theta$$?

$$\sec \theta = \sqrt{1 + 49}$$

Q: A ramp rises $$4 ft $$over a horizontal distance of $$15 ft. $$What is $$\sin \theta$$ where $$\theta is $$the angle the ramp makes with the ground?

$$\sin \theta = \dfrac{4}{\sqrt{4^2$ + 15^2$}}$$

Question 1

Given a right triangle with sides $$a = 5$$, $$b = 12$$, and hypotenuse $$c = 13$$, what is the value of $$\sin 	heta$$ where $$	heta is $$the angle adjacent to side $$a$$?

Accepted Answer

$$\sin 	heta = \dfrac{12}{13}$$

Question 2

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

Accepted Answer

$$\cos 	heta = \dfrac{4}{5}$$

Question 3

Which of the following is a correct reciprocal identity?

Accepted Answer

$$	an 	heta = \dfrac{1}{\cot 	heta}$$

Question 4

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

Accepted Answer

$$\sin 	heta = \dfrac{2}{\sqrt{13}}$$

Question 5

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

Accepted Answer

$$\sec 	heta = \dfrac{2}{\sqrt{1 - (1/2)^2$}}$$

Question 6

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 7

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

Accepted Answer

$$	an 	heta = \dfrac{3}{4}$$

Question 8

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

Accepted Answer

$$\cos 	heta = \dfrac{6}{10}$$

Question 9

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

Accepted Answer

$$\csc 	heta = \dfrac{13}{5}$$

Question 10

Which of the following expresses the Complementary Angle Theorem?

Accepted Answer

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

Question 11

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

Accepted Answer

$$\cot 	heta = \dfrac{4}{3}$$

Question 12

If $$	an 	heta = 7$$ and $$	heta is $$acute, what is $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \sqrt{1 + 49}$$

Question 13

A ramp rises $$4 ft $$over a horizontal distance of $$15 ft. $$What is $$\sin 	heta$$ where $$	heta is $$the angle the ramp makes with the ground?

Accepted Answer

$$\sin 	heta = \dfrac{4}{\sqrt{4^2$ + 15^2$}}$$

Question 14

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

Accepted Answer

$$\sin 	heta = \dfrac{12}{13}$$

Question 15

Which of the following is a quotient identity?

Accepted Answer

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

Question 16

If $$\sin 	heta = \dfrac{1}{3}$$ and $$	heta is $$acute, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{1}{\sqrt{8}}$$

Question 17

A surveyor measures the angle of elevation to the top of a building as $$	heta. If $$the distance from the surveyor to the building is $$d$$ and the height of the building is $$h$$, which trigonometric function relates $$h$$, $$d$$, and $$	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{h}{d}$$

Question 18

If $$\sin 	heta = x$$ and $$	heta is $$acute, what is $$\cos 	heta in $$terms of $$x$$?

Accepted Answer

$$\cos 	heta = \sqrt{1 - x^2$}$$

Question 19

Which of the following is true for complementary angles $$A$$ and $$B in a $$right triangle?

Accepted Answer

$$\sin A = \cos B$$

Right Triangle Trigonometry: Trigonometric Functions and Fundamental Identities

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