Find all the solutions in radians to 40sin2theta 17sintheta

Find *all* the solutions *in radians* to 40sin^2(theta) - 17sin(theta) = 12. Round your answers to four decimal places. Show all steps.

Solution

40sin²theta -17sin theta=12

40sin²theta -17sin theta -12=0

(8sin theta +3)(5sin theta-4)=0

8sin theta +3=0      or       5sin theta -4=0

sin theta=-3/8         or          sin theta=4/5

theta=sin^-1(-3/8)     or             theta=sin^-1(4/5)

theta= 202.02 degree,337.98 degree      or theta= 233.13 degree,306.87 degree

theta=3.53 radian,5.9 radian,4.07 radian,5.36 radian