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

The general solution for 2sin^2(x)-3cos(x)-3=0 is x=pi+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 >

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

2 sin^{2} (x) - 3 cos (x) - 3 = 0

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

Solution steps

2 sin^{2} (x) - 3 cos (x) - 3 = 0

Rewrite using trig identities

- 1 - 2 cos^{2} (x) - 3 cos (x) = 0

Solve by substitution

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

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

3 sin^{2} (x) = cos^{2} (x) - 4 cos (x)

cos (x) = 0.9224

- 9 sin^{2} (θ) + 3 cos (θ) - 2 = - 9

4 sin (x) = 4 cos (x)

sin (θ) + cos (θ) = - 1

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