Solve the equation by factoring.

Question

4sin(θ)cos(θ) + 2 sin(θ) - 2 cos(θ)-1 =0

θ=?

Answer 1

4sinxcos + 2sinx - 2cosx - 1 = 0

2sinx(2cos +1) - (2cosx +1) = 0

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

set each factor =0

sinx=1/2, cosx =-1/2

x = 30 degrees, 150 degrees. Add 360n to each where n= any integer

x =30+360n or 150+360n degrees

or using cosx =-1/2

x = 120 +360n or 240 +360n degrees where n = any integer

4 basic solutions, with reference angles 60 or 30 degrees, pi/3 or pi/6

30, 120, 150 or 240, each with +360n

or in radians pi/6, 2pi/3, 5pi/6 or 4pi/3, each +2npi where n=any integer