Math Core

This test covers trig functions of any angle, exact unit circle values, and the signs of the trig functions in each quadrant.

Question 1

The terminal side of $\theta$ passes through $(-8, 6)$ . Find $\sin\theta$ .

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

Question 2

The terminal side of $\theta$ passes through $(5, -12)$ . Find $\sec\theta$ .

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

Question 3

Find $\cos 270^\circ$ .

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

Question 4

Find $\cot 180^\circ$ . If it is undefined, type "undefined".

Type your answer

Question 5

Find the exact value of $\sin\dfrac{3\pi}{4}$ .

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

Question 6

Find the exact value of $\cos\dfrac{7\pi}{6}$ .

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

Question 7

Find the exact value of $\tan 300^\circ$ .

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

Question 8

Give the exact coordinates of the point where the terminal side of $210^\circ$ meets the unit circle.

Enter a point like (2, -3)

Question 9

Find the exact value of $\sec\dfrac{5\pi}{3}$ .

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

Question 10

Find the exact value of $\sin\left(-\dfrac{13\pi}{6}\right)$ .

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

Question 11

In which quadrant is $\theta$ if $\tan\theta < 0$ and $\cos\theta < 0$ ?

Question 12

Which value is positive?

Question 13

If $\sin\theta = -\dfrac{5}{13}$ and $\theta$ is in Quadrant III, find $\cos\theta$ .

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

Question 14

If $\cot\theta = -2$ and $\cos\theta > 0$ , find the exact value of $\sin\theta$ .

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