Trig Equation

Question

Solve the trig equation -2sin²x=7cosx+2 for 0≤x<π (all angles are in radians)

Answer 1

-2sin²x = 7cosx + 2

 

-2sin²x - 7cosx - 2 = 0

 

-2(1 - cos²x) - 7cosx - 2 = 0

 

2cos²x - 7cosx - 4 = 0

 

(2cosx + 1)(cosx - 4) = 0

 

cosx = -1/2 or cosx = 4

 

The equation cosx = 4 has no solution because -1 ≤ cosx ≤ 1

 

So, cosx = -1/2 and 0 ≤ x < π.  Therefore, x lies in quadrant 2.

 

          x = π - cos^-1(1/2) = π - π/3 = 2π/3