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

The general solution for solvefor x,2cos^2(x)-cos(x)-1=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x,2cos^2(x)-cos(x)-1=0

solve for

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

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

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

- 8 cos (- 4 θ + 150) = 43

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

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

- sin (t) = cos (t)

1 = sin (x^{2})

What is the general solution for solvefor x,2cos^2(x)-cos(x)-1=0 ?
The general solution for solvefor x,2cos^2(x)-cos(x)-1=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin