What is the general solution for sin(2x)-3cos(x)=0 ?

The general solution for sin(2x)-3cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)-3cos(x)=0

sin (2 x) - 3 cos (x) = 0

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

Solution steps

sin (2 x) - 3 cos (x) = 0

Rewrite using trig identities

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

Factor

- 3 cos (x) + 2 cos (x) sin (x) : cos (x) (2 sin (x) - 3)

cos (x) (2 sin (x) - 3) = 0

Solving each part separately

cos (x) = 0 or 2 sin (x) - 3 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin (x) - 3 = 0 :

No Solution

Combine all the solutions

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

5 cos (x) + 1 = 1

cosh (z) = 1

cos (2 x - \frac{π}{6}) = - \frac{1}{2}, \frac{π}{2} < x < π

sin (2 θ) + sin (θ) + 2 cos (θ) + 1 = 0

tan (θ) = \frac{563}{2000}

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