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

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

Q: If $$\\tan(\\theta) = -1$$ and $$0 \u003c \\theta \u003c 2\\pi$$, what are the possible values for $$\\theta$$?

$$\\frac{3\\pi}{4}, \\frac{7\\pi}{4}$$

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

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

Q: If $$\\sin(\\theta) = -\\frac{\\sqrt{2}}{2}$$ and $$0 \u003c \\theta \u003c 2\\pi$$, what are the possible values for $$\\theta$$?

$$\\frac{5\\pi}{4}, \\frac{7\\pi}{4}$$

Question 1

Which of the following best describes a coterminal angle to $$370^\circ$$?

Accepted Answer

$$10^\circ$$

Question 2

A right triangle has legs of length 5 and 5. What is the length of the hypotenuse?

Accepted Answer

$$5\sqrt{2}$$

Question 3

Convert $$540^\circ to $$radians.

Accepted Answer

$$3\pi$$

Question 4

Which of the following is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 5

If $$\sin(\theta) = \frac{3}{5}$$ and $$\theta is in $$Quadrant II, what is $$\cos(\theta)$$?

Accepted Answer

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

Question 6

A hiking path rises 500 feet over a horizontal distance of 4000 feet. What is the angle of inclination of the path? (Round to the nearest degree.)

Accepted Answer

$$7^\circ$$

Question 7

Which of the following is the correct value for $$\tan(45^\circ)$$?

Accepted Answer

$$1$$

Question 8

Given $$\cos(\theta) = -\frac{1}{2}$$ and $$0 \u003c \theta \u003c 2\pi$$, which quadrant(s) could $$\theta be in$$?

Accepted Answer

Quadrant II and III

Question 9

What is the sine of $$30^\circ$$?

Accepted Answer

$$\frac{1}{2}$$

Question 10

A right triangle has an angle of $$31^\circ$$ and a hypotenuse of 8.0. What is the length of the side adjacent to the $$31^\circ$$ angle? (Round to 3 decimal places.)

Accepted Answer

$$6.857$$

Question 11

Which of the following is the correct cofunction identity for $$\sin(\theta)$$?

Accepted Answer

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

Question 12

If $$\tan(\theta) = -1$$ and $$0 \u003c \theta \u003c 2\pi$$, what are the possible values for $$\theta$$?

Accepted Answer

$$\frac{3\pi}{4}, \frac{7\pi}{4}$$

Question 13

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

Accepted Answer

$$\frac{1}{2}$$

Question 14

A sailboat is observed from a lighthouse 240 ft tall, 2.2 km inland from the shore. If the angle of elevation to the top of the lighthouse from the boat is $$3.4^\circ$$, how far is the boat from the coastline? (Round to two decimal places.)

Accepted Answer

$$3.89 km$$

Question 15

Which of the following is the reciprocal identity for $$\sec(\theta)$$?

Accepted Answer

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

Question 16

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^\circ$$

Question 17

If $$\sin(\theta) = -\frac{\sqrt{2}}{2}$$ and $$0 \u003c \theta \u003c 2\pi$$, what are the possible values for $$\theta$$?

Accepted Answer

$$\frac{5\pi}{4}, \frac{7\pi}{4}$$

Question 18

Which of the following is NOT a possible positive angle in standard position?

Accepted Answer

$$-54^\circ$$

Question 19

Given $$\tan(\theta) = \frac{1}{\sqrt{3}}$$, what is $$\theta in $$degrees in the interval $$[0^\circ, 90^\circ]$$?

Accepted Answer

$$30^\circ$$

Angles and the Trigonometric Functions: Comprehensive Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard