Math Core

This test covers radian measure and arc length, the unit circle, the graphs of sine and cosine and their transformations, the tangent function, and the basic trigonometric identities.

Question 1

Convert $240^\circ$ to radians. Give an exact answer in terms of $\pi$ .

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

Question 2

Convert $\dfrac{5\pi}{12}$ radians to degrees.

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

Question 3

A circle has radius $12$ inches. Find the length of the arc cut off by a central angle of $\dfrac{5\pi}{6}$ . Give an exact answer in terms of $\pi$ .

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

Question 4

Find the exact value of $\cos\dfrac{5\pi}{4}$ .

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

Question 5

Find the exact value of $\sin\dfrac{11\pi}{6}$ .

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

Question 6

The terminal side of $\theta$ passes through $(-8, -15)$ . Find $\sin\theta$ .

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

Question 7

If $\tan\theta > 0$ and $\sin\theta < 0$ , in which quadrant does the terminal side of $\theta$ lie?

Question 8

Find all solutions of $\cos x = 0$ on the interval $0 \le x \le 2\pi$ .

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

Question 9

What is the period of $y = -2\sin(3x) + 4$ ?

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

Question 10

What is the minimum value of $y = -2\sin(3x) + 4$ ?

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

Question 11

Which equation matches the graph?

y = 2cos(2x) - 1Open in grapher →

Question 12

Find the exact value of $\tan\dfrac{2\pi}{3}$ .

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

Question 13

What is the period of $y = 4\tan\left(\dfrac{x}{3}\right)$ ?

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

Question 14

Suppose $\sin\theta = -\dfrac{2}{3}$ and $\theta$ is in Quadrant III. Find the exact value of $\cos\theta$ .

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

Question 15

Which expression is equivalent to $\dfrac{\sec x - \cos x}{\sin x}$ ?