What is the general solution for solvefor x,y=5sin(x/4) ?

The general solution for solvefor x,y=5sin(x/4) is x=4arcsin(y/5)+8pin,x=4pi+4arcsin(-y/5)+8pin

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solvefor x,y=5sin(x/4)

solve for

x, y = 5 sin (\frac{x}{4})

x = 4 arcsin (\frac{y}{5}) + 8 πn, x = 4 π + 4 arcsin (- \frac{y}{5}) + 8 πn

Solution steps

y = 5 sin (\frac{x}{4})

Switch sides

5 sin (\frac{x}{4}) = y

Divide both sides by

5

sin (\frac{x}{4}) = \frac{y}{5}

Apply trig inverse properties

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

Solve

\frac{x}{4} = arcsin (\frac{y}{5}) + 2 πn : x = 4 arcsin (\frac{y}{5}) + 8 πn

Solve

\frac{x}{4} = π + arcsin (- \frac{y}{5}) + 2 πn : x = 4 π + 4 arcsin (- \frac{y}{5}) + 8 πn

x = 4 arcsin (\frac{y}{5}) + 8 πn, x = 4 π + 4 arcsin (- \frac{y}{5}) + 8 πn

3 sin (\frac{π}{3} x) = 2

cos^{2} (x) = \frac{1}{3}

4 cos (θ) = 1 + 2 cos (θ)

tan (θ) = \frac{3}{3}

2 sin (3 x) + 2 = 4

What is the general solution for solvefor x,y=5sin(x/4) ?
The general solution for solvefor x,y=5sin(x/4) is x=4arcsin(y/5)+8pin,x=4pi+4arcsin(-y/5)+8pin