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Popular Trigonometry >

solvefor t,g=sin(2pift)

Solution

solve for

t, g = sin (2 π f t)

Solution

t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}, t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}

Solution steps

g = sin (2 π f t)

Switch sides

sin (2 π f t) = g

Apply trig inverse properties

sin (2 π f t) = g

General solutions for

sin (2 π f t) = g

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

2 π f t = arcsin (g) + 2 πn, 2 π f t = π + arcsin (- g) + 2 πn

2 π f t = arcsin (g) + 2 πn, 2 π f t = π + arcsin (- g) + 2 πn

Solve

2 π f t = arcsin (g) + 2 πn : t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}; f \neq = 0

2 π f t = arcsin (g) + 2 πn

Divide both sides by

2 π f; f \neq = 0

2 π f t = arcsin (g) + 2 πn

Divide both sides by

2 π f; f \neq = 0

\frac{2 π f t}{2 π f} = \frac{arcsin ( g )}{2 π f} + \frac{2 πn}{2 π f}; f \neq = 0

Simplify

\frac{2 π f t}{2 π f} = \frac{arcsin ( g )}{2 π f} + \frac{2 πn}{2 π f}

Simplify

\frac{2 π f t}{2 π f} : t

\frac{2 π f t}{2 π f}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t f}{π f}

Cancel the common factor:

π

= \frac{t f}{f}

Cancel the common factor:

f

= t

Simplify

\frac{arcsin ( g )}{2 π f} + \frac{2 πn}{2 π f} : \frac{arcsin ( g )}{2 π f} + \frac{n}{f}

\frac{arcsin ( g )}{2 π f} + \frac{2 πn}{2 π f}

Cancel

\frac{2 πn}{2 π f} : \frac{n}{f}

\frac{2 πn}{2 π f}

Cancel

\frac{2 πn}{2 π f} : \frac{n}{f}

\frac{2 πn}{2 π f}

Divide the numbers:

\frac{2}{2} = 1

= \frac{πn}{π f}

Cancel the common factor:

π

= \frac{n}{f}

= \frac{n}{f}

= \frac{arcsin ( g )}{2 π f} + \frac{n}{f}

t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}; f \neq = 0

t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}; f \neq = 0

t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}; f \neq = 0

Solve

2 π f t = π + arcsin (- g) + 2 πn : t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}; f \neq = 0

2 π f t = π + arcsin (- g) + 2 πn

Divide both sides by

2 π f; f \neq = 0

2 π f t = π + arcsin (- g) + 2 πn

Divide both sides by

2 π f; f \neq = 0

\frac{2 π f t}{2 π f} = \frac{π}{2 π f} + \frac{arcsin ( - g )}{2 π f} + \frac{2 πn}{2 π f}; f \neq = 0

Simplify

\frac{2 π f t}{2 π f} = \frac{π}{2 π f} + \frac{arcsin ( - g )}{2 π f} + \frac{2 πn}{2 π f}

Simplify

\frac{2 π f t}{2 π f} : t

\frac{2 π f t}{2 π f}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t f}{π f}

Cancel the common factor:

π

= \frac{t f}{f}

Cancel the common factor:

f

= t

Simplify

\frac{π}{2 π f} + \frac{arcsin ( - g )}{2 π f} + \frac{2 πn}{2 π f} : \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}

\frac{π}{2 π f} + \frac{arcsin ( - g )}{2 π f} + \frac{2 πn}{2 π f}

Cancel

\frac{π}{2 π f} : \frac{1}{2 f}

\frac{π}{2 π f}

Cancel the common factor:

π

= \frac{1}{2 f}

= \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{2 πn}{2 π f}

Cancel

\frac{2 πn}{2 π f} : \frac{n}{f}

\frac{2 πn}{2 π f}

Cancel

\frac{2 πn}{2 π f} : \frac{n}{f}

\frac{2 πn}{2 π f}

Divide the numbers:

\frac{2}{2} = 1

= \frac{πn}{π f}

Cancel the common factor:

π

= \frac{n}{f}

= \frac{n}{f}

= \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}

t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}; f \neq = 0

t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}; f \neq = 0

t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}; f \neq = 0

t = \frac{arcsin ( g )}{2 π f} + \frac{n}{f}, t = \frac{1}{2 f} + \frac{arcsin ( - g )}{2 π f} + \frac{n}{f}

Graph

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