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

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

cos^{2} (x) + cos (x) - 1 = 0

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

Solution steps

cos^{2} (x) + cos (x) - 1 = 0

Solve by substitution

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

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

cos (x) = \frac{- 1 - 5}{2} :

No Solution

Combine all the solutions

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

Show solutions in decimal form

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

2 = sec (x)

sin (\frac{x}{2} - \frac{π}{3}) = \frac{1}{2}

2 tan (x) + sec (x) = 0, 0 \leq x < 2 π

1 - sin (x) = 3 cos (x)

cos (x) - sec (x) = 0

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