# Precalculus

7.4

#20 use an identity to write each expression as a single trigonometric function value or as a single number.

1-2sin^2(22)(1/2degree)

#30 express each function as a trigonometric function of x. cos 3x

#56 write each expression as a sum or difference of trigonometric functions.

8 sin 7x sin 9x

#58 write each expression as a product of trigonometric functions.

cos 5x + cos 8x

#72 use a half-angle identity to find each exact value. tan 195degrees

7.5

#38 give the degree measure of (theta). (theta)=arcsin(-((â??2)/(2)))

7.6

#64 solve each equation for exact solutions over the interval (0,2(pi))

2â??3 sin 2x = â??3

#76 solve each equation for exact solutions over the interval (0degrees, 360degrees). -2 cos 2(theta)=â??3

7.7

#32 solve each equation for exact solutions. arctan x = arccos (5/13)

#38 solve each equation for exact solutions. arccos x + 2 arcsin (â??3/2)=((pi)/3)

https://brainmass.com/math/basic-calculus/precalculus-374729

#### Solution Preview

(20) 1 - 2 sin^2 (22 1/2) = cos 2(22 1/2) = cos 45 = (1/2) sqrt(2)

(30) cos 3x = 4 cos^3 x - 3 cos x

(56) 8 sin 7x sin 9x = 4(2 sin 9x sin 7x) = 4 [cos 2x - cos 16x]

[Since 2 sin(C + D)/2 sin(C - D)/2 = cos (C - D) - cos (C + D)]

(58) cos 5x + cos 8x = 2 cos (13x/2) cos (3x/2) [Since cos (C + D) + cos (C - D) = 2 cos (C + D)/2 cos (C - D)/2]

(72) tan 195 = tan(180 + 15) = tan 15

tan 2x = 2 tan x / ...

#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided.