What is the general solution for 100=(50)/(sin(x/2)) ?

The general solution for 100=(50)/(sin(x/2)) is x= pi/3+4pin,x=(5pi)/3+4pin

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100=(50)/(sin(x/2))

100 = \frac{50}{sin ( \frac{x}{2} )}

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

Solution steps

100 = \frac{50}{sin ( \frac{x}{2} )}

Switch sides

\frac{50}{sin ( \frac{x}{2} )} = 100

Multiply both sides by

sin (\frac{x}{2})

50 = 100 sin (\frac{x}{2})

Switch sides

100 sin (\frac{x}{2}) = 50

Divide both sides by

100

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

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

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

General solutions for

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

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

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

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

tan (2 θ) = \frac{- 2}{1 - 1}

3 - 3 cos (x) = 3

cos (x) = \frac{5}{6}, \frac{3 π}{2} \leq x \leq 2 π

tan (2 x - 3) = - 1

2 sin^{2} (x) + 5 cos (x) - 3 = 0

What is the general solution for 100=(50)/(sin(x/2)) ?
The general solution for 100=(50)/(sin(x/2)) is x= pi/3+4pin,x=(5pi)/3+4pin