Math Core

This test covers the fundamental identities, verifying identities, the sum and difference formulas, the double-angle and half-angle formulas, and the product-to-sum and sum-to-product formulas.

Question 1

If $\sin\theta = -\dfrac{8}{17}$ and $\theta$ is in Quadrant IV, find $\cos\theta$ .

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

Question 2

Which expression is equal to $\dfrac{\sec^2 x - 1}{\sec^2 x}$ ?

Question 3

The expression $(\sec x - \tan x)(\sec x + \tan x)$ equals a constant wherever it is defined. What is that constant?

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

Question 4

Which equation is not an identity?

Question 5

A student is verifying $\dfrac{1 + \tan^2 x}{\tan^2 x} = \csc^2 x$ . Which chain of steps is correct?

Question 6

Find the exact value of $\sin 105^\circ$ .

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

Question 7

Find the exact value of $\sin 80^\circ \cos 20^\circ - \cos 80^\circ \sin 20^\circ$ .

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

Question 8

If $\tan A = 3$ and $\tan B = \dfrac{1}{2}$ , find $\tan(A - B)$ .

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

Question 9

If $\sin\theta = \dfrac{3}{5}$ and $\theta$ is in Quadrant II, find $\sin 2\theta$ .

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

Question 10

If $\cos\theta = -\dfrac{1}{4}$ , find $\cos 2\theta$ .

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

Question 11

Which expression is equal to $\dfrac{\sin 2x}{2\sin x}$ (where $\sin x \ne 0$ )?

Question 12

Find the exact value of $\cos 22.5^\circ$ .

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

Question 13

If $\cos\theta = \dfrac{1}{9}$ and $270^\circ < \theta < 360^\circ$ , find $\cos\dfrac{\theta}{2}$ .

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

Question 14

Find the exact value of $\sin 15^\circ \cos 75^\circ$ .

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

Question 15

Which expression is equal to $\cos 5x + \cos x$ ?