What is the general solution for 3cos^2(θ)-1=2cos(θ) ?

The general solution for 3cos^2(θ)-1=2cos(θ) is θ=2pin,θ=1.91063…+2pin,θ=-1.91063…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos^2(θ)-1=2cos(θ)

3 cos^{2} (θ) - 1 = 2 cos (θ)

θ = 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

Solution steps

3 cos^{2} (θ) - 1 = 2 cos (θ)

Solve by substitution

cos (θ) = 1, cos (θ) = - \frac{1}{3}

cos (θ) = 1 : θ = 2 πn

cos (θ) = - \frac{1}{3} : θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

Combine all the solutions

θ = 2 πn, θ = arccos (- \frac{1}{3}) + 2 πn, θ = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = 1.91063 \dots + 2 πn, θ = - 1.91063 \dots + 2 πn

cos (\frac{x}{2}) = sin (x)

4 sin^{2} (x) - 5 sin (x) + 1 = 0

tan (x) = - 0.6293

2 cos (\frac{2 x}{3}) - 3 = 0

- sin (2 x) - sin (x) = 0

What is the general solution for 3cos^2(θ)-1=2cos(θ) ?
The general solution for 3cos^2(θ)-1=2cos(θ) is θ=2pin,θ=1.91063…+2pin,θ=-1.91063…+2pin