Trigonometric Equations

Question

Find all solutions, in degrees, to the following equation:
sin2x + 4sinx - 2.25 = 0
The answer is x=__?__ + 2kπ or x = __?__ + 2kπ, where k is any integer.

Give the expressions in the interval [0,2π)

Answer 1

sin²x + 4sinx - 2.25 = 0             Complete the square

sin²x + 4sinx          = 2.25

sin²x + 4sinx + 4    = 2.25 + 4

(sinx + 2)²             = 6.25

sinx + 2                 = ±2.5

 

sinx = -4.25     Impossible

 

sinx = 0.5

 

{π/6, 5π/6}