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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Popular >

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

Solution

solve for

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

Solution

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

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

Divide both sides by

5

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

\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

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

Multiply both sides by

4

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

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

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

4 arcsin (\frac{y}{5}) + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 4 arcsin (\frac{y}{5}) + 8 πn

x = 4 arcsin (\frac{y}{5}) + 8 πn

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

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

Multiply both sides by

4

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

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

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

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

Multiply the numbers:

4 \cdot 2 = 8

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

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

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

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

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Frequently Asked Questions (FAQ)

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