What is the general solution for 2sin(1/2 x)+sqrt(3)=0 ?

The general solution for 2sin(1/2 x)+sqrt(3)=0 is x=(8pi)/3+4pin,x=(10pi)/3+4pin

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2sin(1/2 x)+sqrt(3)=0

2 sin (\frac{1}{2} x) + 3 = 0

x = \frac{8 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

2 sin (\frac{1}{2} x) + 3 = 0

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{4 π}{3} + 2 πn, \frac{1}{2} x = \frac{5 π}{3} + 2 πn

Solve

\frac{1}{2} x = \frac{4 π}{3} + 2 πn : x = \frac{8 π}{3} + 4 πn

Solve

\frac{1}{2} x = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

0 = - \frac{1}{7} cos (7 t)

cos (α) = \frac{5}{13}

tan (x) = 3, 0 \leq x \leq 2 π

3 sec (θ) + 7 = 0

(tan (x) + 1) (sec (x) - 1) = 0

What is the general solution for 2sin(1/2 x)+sqrt(3)=0 ?
The general solution for 2sin(1/2 x)+sqrt(3)=0 is x=(8pi)/3+4pin,x=(10pi)/3+4pin