solving trigonometric equation

Question

How would you solve the following trigonometric equation:

 

5sin^2  x +3sinx =2  -360<O<360

for the first part the sine is being squared by 2 and the whole part ( 5sin^2) is being multiplied by x, just to be clear,

 

appreciate all the help.

Answer 1

Let u = sinx

 

Then, the equation becomes 5u² + 3u - 2 = 0

 

                                        (5u - 2)(u + 1) = 0

 

u = 2/5  or u = -1

 

So, sinx = 2/5 or sinx = -1

 

If sinx = -1, then x = 270°, -90°

 

If sinx = 2/5, sin^-1(2/5) = 23.6°

 

       x = 23.6°, 180°-23.6° are the solutions between 0° and 360°

 

          = 23.6°, 156.4°

 

       Subtract 360° from each of these solutions to obtain two more               solutions in the given interval.