What is the general solution for 4sin^2(x/3)=1 ?

The general solution for 4sin^2(x/3)=1 is x= pi/2+6pin,x=(5pi)/2+6pin,x=(7pi)/2+6pin,x=(11pi)/2+6pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4sin^2(x/3)=1

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

x = \frac{π}{2} + 6 πn, x = \frac{5 π}{2} + 6 πn, x = \frac{7 π}{2} + 6 πn, x = \frac{11 π}{2} + 6 πn

Solution steps

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

Solve by substitution

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

sin (\frac{x}{3}) = \frac{1}{2} : x = \frac{π}{2} + 6 πn, x = \frac{5 π}{2} + 6 πn

sin (\frac{x}{3}) = - \frac{1}{2} : x = \frac{7 π}{2} + 6 πn, x = \frac{11 π}{2} + 6 πn

Combine all the solutions

x = \frac{π}{2} + 6 πn, x = \frac{5 π}{2} + 6 πn, x = \frac{7 π}{2} + 6 πn, x = \frac{11 π}{2} + 6 πn

cos (2 x - \frac{π}{4}) = \frac{2}{2}

sin (5 t) - 1 = 0

2 sin (θ) cos (θ) - sin (θ) = 0

9 sin (x) tan (x) - 2 tan (x) = 0

3 cot (3 x) + 1 = 0

What is the general solution for 4sin^2(x/3)=1 ?
The general solution for 4sin^2(x/3)=1 is x= pi/2+6pin,x=(5pi)/2+6pin,x=(7pi)/2+6pin,x=(11pi)/2+6pin