Math Core

This test covers solving basic trig equations, equations with multiple and shifted angles, and equations that need identities. Unless a problem says otherwise, give exact answers on $[0, 2\pi)$ .

Question 1

Solve $2\sin x + \sqrt{3} = 0$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 2

Solve $\tan\theta = -1$ on $[0^\circ, 360^\circ)$ . Give your answers in degrees.

Separate answers with commas, e.g. 2, -5

Question 3

Solve $\cos\theta = 0.6$ on $[0^\circ, 360^\circ)$ . Round each answer to the nearest tenth of a degree.

Separate answers with commas, e.g. 2, -5

Question 4

Which equation has no solution?

Question 5

Which is the general solution of $2\cos x = \sqrt{3}$ ? ( $k$ is any integer.)

Question 6

Solve $2\sin^2 x - \sin x = 0$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 7

Solve $\sin 2x = -1$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 8

Solve $\cos 3\theta = 0$ on $[0^\circ, 360^\circ)$ . Give your answers in degrees.

Separate answers with commas, e.g. 2, -5

Question 9

How many solutions does $\tan 3x = 2$ have on $[0, 2\pi)$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

Solve $2\cos\left(x - \dfrac{\pi}{4}\right) = \sqrt{2}$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 11

The depth of water at a dock is $d(t) = 6 + 2\sin\left(\dfrac{\pi t}{6}\right)$ feet, $t$ hours after midnight. For $0 \le t < 12$ , at what times is the water $7$ feet deep? Give the values of $t$ .

Separate answers with commas, e.g. 2, -5

Question 12

Solve $2\cos^2 x + 3\sin x - 3 = 0$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 13

Solve $\cos 2x + \cos x + 1 = 0$ on $[0, 2\pi)$ .

Separate answers with commas, e.g. 2, -5

Question 14

Solve $\sin x + \cos x = -1$ on $[0, 2\pi)$ . (If you square both sides, check every answer.)

Separate answers with commas, e.g. 2, -5