What is the general solution for sqrt(3)=sqrt(3)cos(2θ)+sin(2θ) ?

The general solution for sqrt(3)=sqrt(3)cos(2θ)+sin(2θ) is θ=2pin,θ=pi+2pin,θ= pi/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(3)=sqrt(3)cos(2θ)+sin(2θ)

3 = 3 cos (2 θ) + sin (2 θ)

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{6} + πn

Solution steps

3 = 3 cos (2 θ) + sin (2 θ)

Switch sides

3 cos (2 θ) + sin (2 θ) = 3

Subtract

3

from both sides

3 cos (2 θ) + sin (2 θ) - 3 = 0

Rewrite using trig identities

2 cos (θ) sin (θ) - 2 sin^{2} (θ) 3 = 0

Factor

2 cos (θ) sin (θ) - 2 sin^{2} (θ) 3 : 2 sin (θ) (cos (θ) - 3 sin (θ))

2 sin (θ) (cos (θ) - 3 sin (θ)) = 0

Solving each part separately

sin (θ) = 0 or cos (θ) - 3 sin (θ) = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

cos (θ) - 3 sin (θ) = 0 : θ = \frac{π}{6} + πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{6} + πn

8 sin^{2} (x) = sin (x)

6 cos (x) + 6 sin (x) = 36

3 sin (x) + 1 = 0

(tan (x) + 1) (cos (x) - 1) = 0

cot (θ) = - \frac{1}{3}

What is the general solution for sqrt(3)=sqrt(3)cos(2θ)+sin(2θ) ?
The general solution for sqrt(3)=sqrt(3)cos(2θ)+sin(2θ) is θ=2pin,θ=pi+2pin,θ= pi/6+pin