15cos^x=13 + sinx

Question

15cos^x=13 + sinx

Answer 1

Assuming that you mean 15cos²x = 13 + sinx 

 

Then, 15cos²x - sinx - 13 = 0

 

15(1 - sin²x) - sinx - 13 = 0

 

-15sin²x - sinx + 2 = 0

 

15sin²x + sinx - 2 = 0

 

(5sinx + 2)(3sinx -1) = 0

 

So, sinx = -2/5 or sinx = 1/3

 

If sin x = -2/5, then x lies in Quadrant 3 or 4

 

     sin^-1(2/5) = 23.6°  

     So, x = 180°+23.6° = 203.6° or

           x = 360°-23.6° = 336.4°

 

If sin x = 1/3, then x lies in Quadrant 1 or 2

 

     sin^-1(1/3) = 19.5°

     So, x = 19.5° or 180° - 19.5° = 160.5°

 

The solutions between 0° and 360° are approximately:

      19.5°, 160.5°, 203.6°, 336.4°

 

NOTE:  If you need the answers to be in radians, multiply             each of the four given answers by π/180.