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Popular >

solvefor t,L{sin(2t)}= 2/(s^2+4)

Solution

solve for

t, L {sin (2 t)} = \frac{2}{s ^{2} + 4}

Solution

t = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn, t = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

Solution steps

L {sin (2 t)} = \frac{2}{s ^{2} + 4}

Divide both sides by

L

L {sin (2 t)} = \frac{2}{s ^{2} + 4}

Divide both sides by

L

\frac{L { sin ( 2 t ) }}{L} = \frac{\frac{2}{s ^{2} + 4}}{L}

Simplify

\frac{L { sin ( 2 t ) }}{L} = \frac{\frac{2}{s ^{2} + 4}}{L}

Simplify

\frac{L ( sin ( 2 t ) )}{L} : sin (2 t)

\frac{L { sin ( 2 t ) }}{L}

Remove parentheses:

(a) = a

= \frac{L sin ( 2 t )}{L}

Cancel the common factor:

L

= sin (2 t)

Simplify

\frac{\frac{2}{s ^{2} + 4}}{L} : \frac{2}{L ( s ^{2} + 4 )}

\frac{\frac{2}{s ^{2} + 4}}{L}

Apply the fraction rule:

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

= \frac{2}{( s ^{2} + 4 ) L}

sin (2 t) = \frac{2}{L ( s ^{2} + 4 )}

sin (2 t) = \frac{2}{L ( s ^{2} + 4 )}

sin (2 t) = \frac{2}{L ( s ^{2} + 4 )}

Apply trig inverse properties

sin (2 t) = \frac{2}{L ( s ^{2} + 4 )}

General solutions for

sin (2 t) = \frac{2}{L ( s ^{2} + 4 )}

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

2 t = arcsin (\frac{2}{L ( s ^{2} + 4 )}) + 2 πn, 2 t = π + arcsin (- \frac{2}{L ( s ^{2} + 4 )}) + 2 πn

2 t = arcsin (\frac{2}{L ( s ^{2} + 4 )}) + 2 πn, 2 t = π + arcsin (- \frac{2}{L ( s ^{2} + 4 )}) + 2 πn

Solve

2 t = arcsin (\frac{2}{L ( s ^{2} + 4 )}) + 2 πn : t = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

2 t = arcsin (\frac{2}{L ( s ^{2} + 4 )}) + 2 πn

Divide both sides by

2

2 t = arcsin (\frac{2}{L ( s ^{2} + 4 )}) + 2 πn

Divide both sides by

2

\frac{2 t}{2} = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + \frac{2 πn}{2}

Simplify

t = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

t = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

Solve

2 t = π + arcsin (- \frac{2}{L ( s ^{2} + 4 )}) + 2 πn : t = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

2 t = π + arcsin (- \frac{2}{L ( s ^{2} + 4 )}) + 2 πn

Divide both sides by

2

2 t = π + arcsin (- \frac{2}{L ( s ^{2} + 4 )}) + 2 πn

Divide both sides by

2

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + \frac{2 πn}{2}

Simplify

t = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

t = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

t = \frac{arcsin ( \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn, t = \frac{π}{2} + \frac{arcsin ( - \frac{2}{L ( s ^{2} + 4 )} )}{2} + πn

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