Solve 5 sin20 8 cos9 0 for all solutions 0 Solution5 sin 2

Solve 5 sin(20) + 8 cos(9) = 0 for all solutions 0

Solution

5 sin 2 theta + 8 cos theta = 0

sin 2 theta = 2 sin theta cos theta

5 ( 2 sin tehta cos theta ) + 8 cos theta = 0

10 sin theta cos theta + 8 cos theta = 0

2 cos theta ( 5 sin theta + 4 ) = 0

2 cos theta = 0

theta = pi/2 , 3pi/2

5 sin theta + 4 = 0

sin theta =-4/5

theta = -0.93 + 2pi , 0.93 + pi

solutions are

theta = pi/2 , 3pi/2 , -0.93 + 2pi , 0.93 + pi

2) 12sin^2 t + 5 sin t - 2 = 0

( 4 sin t - 1 ) ( 3 sin t + 2 )= 0

sin t = 1/4 , sin t = -2/3

t = 3.87 , 5.55 , 2.89 , 0.25