Math Core

This test covers radian measure, the unit circle definitions of the six trig functions, graphs of sinusoids and tangent, and the inverse trigonometric functions.

Question 1

Convert $150^\circ$ to radians.

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

Question 2

A central angle of $3.5$ radians is drawn in a circle of radius $4$ in. How long is the intercepted arc, in inches?

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

Question 3

Find the exact value of $\sin\dfrac{7\pi}{4}$ .

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

Question 4

Find the exact value of $\sec\dfrac{8\pi}{3}$ .

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

Question 5

If $\tan t \lt 0$ and $\sin t \gt 0$ , in which quadrant does the angle $t$ end?

Question 6

Suppose $\cos t = \dfrac{7}{25}$ and $\dfrac{3\pi}{2} \lt t \lt 2\pi$ . Find $\tan t$ .

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

Question 7

Find all $t$ in $[0, 2\pi)$ with $\sin t = -\dfrac{1}{2}$ .

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

Question 8

What is the period of $y = 3\cos\left(\dfrac{x}{2} - \pi\right) + 5$ ?

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

Question 9

Which statement describes $y = -2\sin\left(3x - \dfrac{\pi}{2}\right) + 4$ ?

Question 10

Which equation matches the graph?

Minimum -2 at x = 0; maximums 4 at x = ±π/2.Open in grapher →

Question 11

A sinusoid $y = A\sin(Bx) + D$ with $B > 0$ repeats every $4$ units. Find $B$ .

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

Question 12

Find the vertical asymptotes of $y = \tan\left(\dfrac{x}{3}\right)$ in the interval $(-3\pi, 3\pi)$ .

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

Question 13

Find the exact value of $\arccos\left(-\dfrac{\sqrt{2}}{2}\right)$ .

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

Question 14

Find the exact value of $\arctan\left(\tan\dfrac{2\pi}{3}\right)$ .

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

Question 15

Find the exact value of $\tan\left(\arcsin\left(-\dfrac{3}{5}\right)\right)$ .

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