Question

Solve the following interval
0<_ (less than or equal to)0(Theta)<2pi:

1. sin0(theta) + sin2 0(theta) = 0

2. 2cos^20 (theta) + cos0 (theta) -1 = 0

Answer 1

sinӨ + sin2Ө = 0

recall that sin2Ө = 2sinӨcosӨ

so sinӨ + sin2Ө = 0
sinӨ + 2sinӨcosӨ = 0
sinӨ(1+2cosӨ)=0
sinӨ = 0 or 2cosӨ = -1
sinӨ = 0 or or cosӨ = -1/2

Ө = 0,pi,2pi or Ө=2pi/3,4pi/3

in degrees: 0,180,360,120,240