Math7

1.   Rewrite the following expression as an equivalent expression that doesn't contain powers of trigonometric functions greater than 1. 8cos2x 

2.   Find all solutions to the following equation: sinx csc x = –2 sin x 

3.   Use the given information to find the exact value of the expression.

tan α = 21⁄20, α lies in quadrant III, cos β = –5⁄13, and β lies in quadrant II.

Find sin(α + β). 

4.   Find the exact value by using the sum or difference identity:

cos (135° + 120°) 

5.   Express the following sum or difference as a product: cos 2x – cos 4x 

6.   Complete the following identity:  

7.   Use a calculator to solve the equation on the on the interval [0, 2π). Round the answer to two decimal places. cos x = 0.65 

8.   Find the exact value of the expression:

sin 10° cos 50° + cos 10° sin 50° 

9.   Complete the following identity: (sin x + cos x)2 = _______ 

10.   Find the exact value of the expression:

11.   Show that the following equation is not an identity by finding a value of x for which both sides are defined but not equal.

cos( x + π) = cos x 

12.   Express the following sum or difference as a product: sin 8x + sin 4x 

A. cos x

B. sec x

C. csc x

D. sin x

14.   Find all solutions to the following equation: 2 sin x + 1 = 0 2 sin x + 1 = 0 

15.   Rewrite the expression in terms of the given function: (sec x + csc x )(sin x + cos x) – 2 – tan x; cot x 

16.   Complete the identity:

tan x (cot x – cos x) = _______ 

17.   Use a half-angle formula to find the exact value of the following expression: cos 112.5° 

18.   Use a calculator to solve the equation on the on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 3x = –sinx 

19.   Complete the following identity.  

20.   Find the exact value of the expression:

cos (165°) cos (45°) + sin (165°) sin (45°)