What is the general solution for sin^3(x)= 1/2 ?

The general solution for sin^3(x)= 1/2 is x=0.91686…+2pin,x=pi-0.91686…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^3(x)= 1/2

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

x = 0.91686 \dots + 2 πn, x = π - 0.91686 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

sin (x) = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{2 ^{\frac{2}{3}} 3}{4} :

No Solution

Combine all the solutions

Show solutions in decimal form

x = 0.91686 \dots + 2 πn, x = π - 0.91686 \dots + 2 πn

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

5 sin^{2} (x) - sin (x) = 0

3 sin^{2} (2 x) + 7 cos (2 x) - 3 = 0

3 tan (2 θ) - 1 = 0

3 cos^{2} (θ) - 1 = 2 cos (θ)

What is the general solution for sin^3(x)= 1/2 ?
The general solution for sin^3(x)= 1/2 is x=0.91686…+2pin,x=pi-0.91686…+2pin