What is the general solution for sin(θ)+2sin(θ)cos(θ)=0 ?

The general solution for sin(θ)+2sin(θ)cos(θ)=0 is θ=2pin,θ=pi+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ)+2sin(θ)cos(θ)=0

sin (θ) + 2 sin (θ) cos (θ) = 0

θ = 2 πn, θ = π + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solution steps

sin (θ) + 2 sin (θ) cos (θ) = 0

Factor

sin (θ) + 2 sin (θ) cos (θ) : sin (θ) (2 cos (θ) + 1)

sin (θ) (2 cos (θ) + 1) = 0

Solving each part separately

sin (θ) = 0 or 2 cos (θ) + 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

2 cos (θ) + 1 = 0 : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

x, arcsin (y) - arccos (x) = 1

- 6 = - 2 + 8 sin (θ + \frac{π}{4})

0 = 12 cos (\frac{π}{3} x) + 8

0 = sin (t) + 2 sin (2 t)

sin (x) = - 0.9

What is the general solution for sin(θ)+2sin(θ)cos(θ)=0 ?
The general solution for sin(θ)+2sin(θ)cos(θ)=0 is θ=2pin,θ=pi+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin