What is the general solution for 2sin(1/2 x)+sqrt(2)=0 ?

The general solution for 2sin(1/2 x)+sqrt(2)=0 is x=(5pi)/2+4pin,x=(7pi)/2+4pin

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2sin(1/2 x)+sqrt(2)=0

2 sin (\frac{1}{2} x) + 2 = 0

x = \frac{5 π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

Solution steps

2 sin (\frac{1}{2} x) + 2 = 0

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{5 π}{4} + 2 πn, \frac{1}{2} x = \frac{7 π}{4} + 2 πn

Solve

\frac{1}{2} x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{2} + 4 πn

Solve

\frac{1}{2} x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{2} + 4 πn

x = \frac{5 π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

\frac{cos ( x )}{sin ( x )} = - 0.05467

2 sin^{4} (x) + 2 sin^{2} (x) cos^{2} (x) = 1

(1 + 4 cos (θ))^{2} = (3 sin (θ))^{2}

\frac{1}{tan ( x )} = 4

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

What is the general solution for 2sin(1/2 x)+sqrt(2)=0 ?
The general solution for 2sin(1/2 x)+sqrt(2)=0 is x=(5pi)/2+4pin,x=(7pi)/2+4pin