What is the general solution for -4cos^2(θ)+cos(θ)=9cos(θ)+3 ?

The general solution for -4cos^2(θ)+cos(θ)=9cos(θ)+3 is 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 >

-4cos^2(θ)+cos(θ)=9cos(θ)+3

- 4 cos^{2} (θ) + cos (θ) = 9 cos (θ) + 3

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

Solution steps

- 4 cos^{2} (θ) + cos (θ) = 9 cos (θ) + 3

Solve by substitution

cos (θ) = - \frac{3}{2}, cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{3}{2} :

No Solution

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

Combine all the solutions

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

3 + 4 cot (x) = 5 csc (x)

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

tan (θ) = \frac{9}{10}

tan (x) = \frac{3}{205}

sin (x) sin (2 x) = sin (3 x)

What is the general solution for -4cos^2(θ)+cos(θ)=9cos(θ)+3 ?
The general solution for -4cos^2(θ)+cos(θ)=9cos(θ)+3 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin