What is the general solution for sin^2(x)=|sin(x)| ?

The general solution for sin^2(x)=|sin(x)| is x=(3pi)/2+2pin,x=2pin,x=pi+2pin,x= pi/2+2pin

Popular >

sin^2(x)=|sin(x)|

sin^{2} (x) = ∣ sin (x) ∣

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

Solution steps

sin^{2} (x) = ∣ sin (x) ∣

Solve by substitution

sin (x) = - 1 or sin (x) = 0 or sin (x) = 1

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

1 - cos^{2} (x) - sin^{22} (x) = 0

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

5 cos (x) = 1 + 2 sin^{2} (x)

tan (2 x + 1) = - cot (x + 3)

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

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