Q: Which of the following is the correct formula to convert degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Q: What is the reciprocal identity for $$\sin \theta$$?

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

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

$$10 \times \sin 60^\ ext{o} = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Q: Which of the following is NOT a fundamental trigonometric identity?

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

Q: A ramp rises 2 meters vertically for every 5 meters horizontally. What is the angle of elevation of the ramp?

$$\tan$$^{-1}$$ \left( \frac{2}{5} \right)$$

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

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

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side lies along the positive x-axis.

Question 2

Convert $$120^\	ext{o} to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 3

Which of the following is the correct formula to convert degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Question 4

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

Accepted Answer

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

Question 5

Which trigonometric function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle?

Accepted Answer

$$\cos 	heta$$

Question 6

If $$	an 	heta = \frac{3}{4}$$, what is $$\cot 	heta$$?

Accepted Answer

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

Question 7

What is the reciprocal identity for $$\sin 	heta$$?

Accepted Answer

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

Question 8

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

Accepted Answer

$$10 	imes \sin 60^\	ext{o} = 10 	imes \frac{\sqrt{3}}{2} = 5\sqrt{3} ft$$

Question 9

Which of the following angles is an obtuse angle?

Accepted Answer

$$120^\	ext{o}$$

Question 10

If $$\cos 	heta = \frac{4}{5} in a $$right triangle, what is $$\sec 	heta$$?

Accepted Answer

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

Question 11

A wheel rotates through $$\frac{\pi}{2}$$ radians. How many degrees does it rotate?

Accepted Answer

$$90^\	ext{o}$$

Question 12

Which trigonometric function is used to find the height of a building if you know the distance from the building and the angle of elevation?

Accepted Answer

$$	an 	heta$$

Question 13

If $$\sin 	heta = \frac{3}{5}$$ and $$\cos 	heta = \frac{4}{5}$$, what is $$	an 	heta$$?

Accepted Answer

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

Question 14

Which of the following is NOT a fundamental trigonometric identity?

Accepted Answer

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

Question 15

A triangle has sides of length 5, 12, and 13. What is $$\sin 	heta if$$ $$	heta is $$the angle opposite the side of length 5?

Accepted Answer

$$\frac{5}{13}$$

Question 16

Which trigonometric function is undefined for a $$90^\	ext{o}$$ angle?

Accepted Answer

$$	an 90^\	ext{o}$$

Question 17

If $$	heta is an $$angle in standard position and its terminal side lies on the negative y-axis, what is the measure of $$	heta$$?

Accepted Answer

$$270^\	ext{o}$$

Question 18

A ramp rises 2 meters vertically for every 5 meters horizontally. What is the angle of elevation of the ramp?

Accepted Answer

$$	an$$^{-1}$$ \left( \frac{2}{5} ight)$$

Question 19

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

Accepted Answer

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

Study Notes: Trigonometric Functions (Precalculus, Ch. 5)

Guida di studio - Domande di pratica

Study guide - Flashcard