What is the general solution for cos^2(θ)+cos(θ)-1=0 ?

The general solution for cos^2(θ)+cos(θ)-1=0 is θ=0.90455…+2pin,θ=2pi-0.90455…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(θ)+cos(θ)-1=0

cos^{2} (θ) + cos (θ) - 1 = 0

θ = 0.90455 \dots + 2 πn, θ = 2 π - 0.90455 \dots + 2 πn

Solution steps

cos^{2} (θ) + cos (θ) - 1 = 0

Solve by substitution

cos (θ) = \frac{- 1 + 5}{2}, cos (θ) = \frac{- 1 - 5}{2}

cos (θ) = \frac{- 1 + 5}{2} : θ = arccos (\frac{- 1 + 5}{2}) + 2 πn, θ = 2 π - arccos (\frac{- 1 + 5}{2}) + 2 πn

cos (θ) = \frac{- 1 - 5}{2} :

No Solution

Combine all the solutions

θ = arccos (\frac{- 1 + 5}{2}) + 2 πn, θ = 2 π - arccos (\frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

θ = 0.90455 \dots + 2 πn, θ = 2 π - 0.90455 \dots + 2 πn

sin^{2} (x) - 3 = 0

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

sin (θ) = \frac{- 2}{2}

cos (θ) csc (θ) = - 2 cos (θ)

csc^{2} (x) - 4 cot (x) = - 2

What is the general solution for cos^2(θ)+cos(θ)-1=0 ?
The general solution for cos^2(θ)+cos(θ)-1=0 is θ=0.90455…+2pin,θ=2pi-0.90455…+2pin