What is the general solution for cos(2x)+5cos(x)+3=0 ?

The general solution for cos(2x)+5cos(x)+3=0 is 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 >

cos(2x)+5cos(x)+3=0

cos (2 x) + 5 cos (x) + 3 = 0

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

Solution steps

cos (2 x) + 5 cos (x) + 3 = 0

Rewrite using trig identities

2 + 2 cos^{2} (x) + 5 cos (x) = 0

Solve by substitution

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

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

cos (x) = - 2 :

No Solution

Combine all the solutions

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

2 cos (θ) = 1

sin (x + \frac{π}{6}) - sin (x - \frac{π}{6}) = \frac{1}{2}

tan (θ) = \frac{5}{12}

cos (3 x) = \frac{3}{2}

sin (x) = cos (x) - 1

What is the general solution for cos(2x)+5cos(x)+3=0 ?
The general solution for cos(2x)+5cos(x)+3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin