Trigonometry Question

Question

2sin^2 theta-3 sin theta+1=0

Answer 1

I always find it easier to solve problems like this by substituting x for sin theta

So our equation is 2x^2 -3x +1 =0. This factors to

(2x-1)(x-1)=0

x= 1/2. x=1 which gives sin theta=1/2 and sint theta= 1

The angles that have a sin equal to 1/2 are pie/6 and 5pie/6

The angle with a sin of 1 is pie/2 so our solutions are

pie/6 +2pie(n)

pie/2 +2pie(n)

5pie/6 +2pie(n)