What is the general solution for 2sin(x/2)=sqrt(2) ?

The general solution for 2sin(x/2)=sqrt(2) is x= pi/2+4pin,x=(3pi)/2+4pin

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2sin(x/2)=sqrt(2)

2 sin (\frac{x}{2}) = 2

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

Solution steps

2 sin (\frac{x}{2}) = 2

Divide both sides by

2

sin (\frac{x}{2}) = \frac{2}{2}

General solutions for

sin (\frac{x}{2}) = \frac{2}{2}

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

Solve

\frac{x}{2} = \frac{π}{4} + 2 πn : x = \frac{π}{2} + 4 πn

Solve

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

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

cos (θ) = 0.7071

2 cos (x) - 5 sin (x) = 0

2 cos^{2} (x) = 3 cos (x) + 2

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

tan (2 x) sin (x) - sin (x) - tan (2 x) + 1 = 0

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