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

The general solution for 3sin^2(x)+sin(x)-2=0 is x=0.72972…+2pin,x=pi-0.72972…+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 >

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

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

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{2}{3}, sin (x) = - 1

sin (x) = \frac{2}{3} : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

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

Combine all the solutions

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn, x = \frac{3 π}{2} + 2 πn

Show solutions in decimal form

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

6 sin^{2} (θ) - sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

33 cot (x) = 3

2 tan^{2} (x) - 6 = 0

0 = 2 sin (x) - 1

t, x = cos (2 t)

What is the general solution for 3sin^2(x)+sin(x)-2=0 ?
The general solution for 3sin^2(x)+sin(x)-2=0 is x=0.72972…+2pin,x=pi-0.72972…+2pin,x=(3pi)/2+2pin