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Popular >

solvefor x,y= 1/(5sin(2x))

Solution

solve for

x, y = \frac{1}{5 sin ( 2 x )}

Solution

x = \frac{arcsin ( \frac{1}{5 y} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + πn

Solution steps

y = \frac{1}{5 sin ( 2 x )}

Switch sides

\frac{1}{5 sin ( 2 x )} = y

Multiply both sides by

sin (2 x)

\frac{1}{5 sin ( 2 x )} = y

Multiply both sides by

sin (2 x)

\frac{1}{5 sin ( 2 x )} sin (2 x) = y sin (2 x)

Simplify

\frac{1}{5} = y sin (2 x)

\frac{1}{5} = y sin (2 x)

Switch sides

y sin (2 x) = \frac{1}{5}

Divide both sides by

y; y \neq = 0

y sin (2 x) = \frac{1}{5}

Divide both sides by

y; y \neq = 0

\frac{y sin ( 2 x )}{y} = \frac{\frac{1}{5}}{y}; y \neq = 0

Simplify

\frac{y sin ( 2 x )}{y} = \frac{\frac{1}{5}}{y}

Simplify

\frac{y sin ( 2 x )}{y} : sin (2 x)

\frac{y sin ( 2 x )}{y}

Cancel the common factor:

y

= sin (2 x)

Simplify

\frac{\frac{1}{5}}{y} : \frac{1}{5 y}

\frac{\frac{1}{5}}{y}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1}{5 y}

sin (2 x) = \frac{1}{5 y}; y \neq = 0

sin (2 x) = \frac{1}{5 y}; y \neq = 0

sin (2 x) = \frac{1}{5 y}; y \neq = 0

Apply trig inverse properties

sin (2 x) = \frac{1}{5 y}

General solutions for

sin (2 x) = \frac{1}{5 y}

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

2 x = arcsin (\frac{1}{5 y}) + 2 πn, 2 x = π + arcsin (- \frac{1}{5 y}) + 2 πn

2 x = arcsin (\frac{1}{5 y}) + 2 πn, 2 x = π + arcsin (- \frac{1}{5 y}) + 2 πn

Solve

2 x = arcsin (\frac{1}{5 y}) + 2 πn : x = \frac{arcsin ( \frac{1}{5 y} )}{2} + πn

2 x = arcsin (\frac{1}{5 y}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{1}{5 y}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{5 y} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{1}{5 y} )}{2} + πn

x = \frac{arcsin ( \frac{1}{5 y} )}{2} + πn

Solve

2 x = π + arcsin (- \frac{1}{5 y}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + πn

2 x = π + arcsin (- \frac{1}{5 y}) + 2 πn

Divide both sides by

2

2 x = π + arcsin (- \frac{1}{5 y}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + πn

x = \frac{arcsin ( \frac{1}{5 y} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( - \frac{1}{5 y} )}{2} + πn

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