Solve the equation sin4theta 035 in 0 2 pi Provide exact va

Solve the equation sin(4theta) = -0.35 in [0, 2 pi). Provide exact values and numerical approximations rounded to two decimal places. Show all steps of your solution.

Solution

sin(4)=-0.35

0<=<2

=> 0<=4<8

(4)=2-sin^-1(0.35) ,4-sin^-1(0.35) ,6-sin^-1(0.35) ,8-sin^-1(0.35) ,+sin^-1(0.35),3+sin^-1(0.35),5+sin^-1(0.35),7+sin^-1(0.35),

exact values :

=(_/2)-(1_/4)sin^-1(0.35) ,-(1_/4)sin^-1(0.35) ,(3_/2)-(1_/4)sin^-1(0.35) ,2-(1_/4)sin^-1(0.35) ,(_/4)+(1_/4)sin^-1(0.35),(3_/4)+(1_/4)sin^-1(0.35),(5_/4)+(1_/4)sin^-1(0.35),(7_/4)+(1_/4)sin^-1(0.35),

approximations:

=1.48, 3.05 ,4.62,6.19,0.87,2.45,4.02,5.59