Question 1

Which quadrant does the terminal side of an angle of $$405^\circ$$ lie in when drawn in standard position?

Accepted Answer

Quadrant I

Question 2

Find the least positive angle that is coterminal with $$-144^\circ.$$

Accepted Answer

$$36^\circ$$

Question 3

Convert $$60^\circ to $$radians.

Accepted Answer

$$\frac{\pi}{3}$$ radians

Question 4

Convert $$\frac{7\pi}{6}$$ radians to degrees. Round to two decimal places if needed.

Accepted Answer

$$210^\circ$$

Question 5

Find the measure of the central angle (in radians) of a circle of radius $$1.5$$ feet that intercepts an arc of length $$6$$ feet.

Accepted Answer

$$4$$ radians

Question 6

Assume that two cities lie on the same north-south line and that the radius of the earth is $$6400 km. $$Find the distance between City A, $$60^\circ N $$and City B, $$83.5^\circ N. ($$Round to the nearest kilometer.)

Accepted Answer

$$2592 km$$

Question 7

Use the Pythagorean Theorem to find the missing side of the right triangle with legs $$5$$ and $$12.$$

Accepted Answer

$$13$$

Question 8

Two similar triangles are given. The proportionality constant $$k$$ such that the length of each side of the larger triangle is $$k$$ times the length of the sides of the smaller triangle. If $$k=\sqrt{5}$$, find the length of the missing sides if the smaller triangle has sides $$2$$, $$2\sqrt{5}$$, and $$4.$$

Accepted Answer

$$2\sqrt{5}, 10, 8$$

Question 9

A right triangle with acute angle $$\theta is $$given. If $$\sin \theta = \frac{8}{17}$$, find $$\cos \theta.$$

Accepted Answer

$$\frac{15}{17}$$

Question 10

Evaluate $$\tan \theta$$ for an acute angle $$\theta in a $$right triangle if $$\sin \theta = \frac{5}{13}.$$

Accepted Answer

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

Question 11

A point $$(3, 4)$$ lies on the terminal side of angle $$\theta. $$Find $$\sin \theta.$$

Accepted Answer

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

Question 12

Without using a calculator, determine the value of $$\sin 0.$$

Accepted Answer

$$0$$

Question 13

Determine the quadrant in which the terminal side of angle $$\theta$$ lies if $$\sin \theta \u003c 0$$ and $$\cos \theta \u003c 0.$$

Accepted Answer

Quadrant III

Question 14

Find the value of $$\cos \theta if$$ $$\sin \theta = -\frac{3}{5}$$ and the terminal side of $$\theta$$ lies in Quadrant III.

Accepted Answer

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

Question 15

Determine the reference angle for $$\frac{7\pi}{6}.$$

Accepted Answer

$$\frac{\pi}{6}$$

Question 16

Find the value of $$\sin t if $$the point $$(-\frac{1}{2}, \frac{\sqrt{3}}{2})$$ lies on the unit circle.

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 17

Use the unit circle to determine the value of $$\tan(\frac{\pi}{2}).$$

Accepted Answer

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Question 18

A surveyor is measuring the distance across a small lake. He sets up his transit on one side of the lake, $$150$$ feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is $$65^\circ. $$What is the distance between the piling and the pier to the nearest foot?

Accepted Answer

$$322$$ feet

Question 19

Use identities to find the exact value of $$\cos^2$ 20^\circ + \sin^2$ 20^\circ.$$

Accepted Answer

$$1$$

Precalculus Study Guide: Angles, Trigonometry, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards