What is the general solution for 4cos^2(x)+4cos(x)=1 ?

The general solution for 4cos^2(x)+4cos(x)=1 is x=1.36217…+2pin,x=2pi-1.36217…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(x)+4cos(x)=1

4 cos^{2} (x) + 4 cos (x) = 1

x = 1.36217 \dots + 2 πn, x = 2 π - 1.36217 \dots + 2 πn

Solution steps

4 cos^{2} (x) + 4 cos (x) = 1

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 1.36217 \dots + 2 πn, x = 2 π - 1.36217 \dots + 2 πn

sin (x) = \frac{1}{6}

tan (θ) = \frac{2}{5}

tan (x) + 3 cot (x) = 4

cos (2 x) [cos (2 x) - 3] = 0

cos^{2} (θ) = \frac{1}{4}

What is the general solution for 4cos^2(x)+4cos(x)=1 ?
The general solution for 4cos^2(x)+4cos(x)=1 is x=1.36217…+2pin,x=2pi-1.36217…+2pin