What is the general solution for sin(x/2)= 3/5 ?

The general solution for sin(x/2)= 3/5 is x=2*0.64350…+4pin,x=2pi-2*0.64350…+4pin

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sin(x/2)= 3/5

sin (\frac{x}{2}) = \frac{3}{5}

x = 2 \cdot 0.64350 \dots + 4 πn, x = 2 π - 2 \cdot 0.64350 \dots + 4 πn

Degrees

x = 73.73979 \dots^{\circ} + 72 0^{\circ} n, x = 286.26020 \dots^{\circ} + 72 0^{\circ} n

Solution steps

sin (\frac{x}{2}) = \frac{3}{5}

Apply trig inverse properties

sin (\frac{x}{2}) = \frac{3}{5}

General solutions for

sin (\frac{x}{2}) = \frac{3}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn, \frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn, \frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn

Solve

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn : x = 2 arcsin (\frac{3}{5}) + 4 πn

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn

Multiply both sides by

2

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn : 2 arcsin (\frac{3}{5}) + 4 πn

2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

Solve

\frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn : x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

\frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn

Multiply both sides by

2

\frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 π - 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 π - 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 π - 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn : 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

2 π - 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn, x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

Show solutions in decimal form

x = 2 \cdot 0.64350 \dots + 4 πn, x = 2 π - 2 \cdot 0.64350 \dots + 4 πn

16 cos^{2} (x) - 8 = 0

2 sin (4 θ) = 0

θ, 4 sin^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) - 7 = 0

2 sin^{2} (x) - sin (x) = 0, 0 \leq x \leq 2 π

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

What is the general solution for sin(x/2)= 3/5 ?
The general solution for sin(x/2)= 3/5 is x=2*0.64350…+4pin,x=2pi-2*0.64350…+4pin