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Popular >

solvefor t,fw=2+cos(10pit)

Solution

solve for

t, f w = 2 + cos (10 π t)

Solution

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}, t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

Solution steps

f w = 2 + cos (10 π t)

Switch sides

2 + cos (10 π t) = f w

Move

2

to the right side

2 + cos (10 π t) = f w

Subtract

2

from both sides

2 + cos (10 π t) - 2 = f w - 2

Simplify

cos (10 π t) = f w - 2

cos (10 π t) = f w - 2

Apply trig inverse properties

cos (10 π t) = f w - 2

General solutions for

cos (10 π t) = f w - 2

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

10 π t = arccos (f w - 2) + 2 πn, 10 π t = - arccos (f w - 2) + 2 πn

10 π t = arccos (f w - 2) + 2 πn, 10 π t = - arccos (f w - 2) + 2 πn

Solve

10 π t = arccos (f w - 2) + 2 πn : t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

10 π t = arccos (f w - 2) + 2 πn

Divide both sides by

10 π

10 π t = arccos (f w - 2) + 2 πn

Divide both sides by

10 π

\frac{10 π t}{10 π} = \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Simplify

\frac{10 π t}{10 π} = \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Simplify

\frac{10 π t}{10 π} : t

\frac{10 π t}{10 π}

Divide the numbers:

\frac{10}{10} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π} : \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

\frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Cancel

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

Cancel

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

Cancel the common factor:

2

= \frac{πn}{5 π}

Cancel the common factor:

π

= \frac{n}{5}

= \frac{n}{5}

= \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

Solve

10 π t = - arccos (f w - 2) + 2 πn : t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

10 π t = - arccos (f w - 2) + 2 πn

Divide both sides by

10 π

10 π t = - arccos (f w - 2) + 2 πn

Divide both sides by

10 π

\frac{10 π t}{10 π} = - \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Simplify

\frac{10 π t}{10 π} = - \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Simplify

\frac{10 π t}{10 π} : t

\frac{10 π t}{10 π}

Divide the numbers:

\frac{10}{10} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

- \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π} : - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

- \frac{arccos ( f w - 2 )}{10 π} + \frac{2 πn}{10 π}

Cancel

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

Cancel

\frac{2 πn}{10 π} : \frac{n}{5}

\frac{2 πn}{10 π}

Cancel the common factor:

2

= \frac{πn}{5 π}

Cancel the common factor:

π

= \frac{n}{5}

= \frac{n}{5}

= - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

t = \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}, t = - \frac{arccos ( f w - 2 )}{10 π} + \frac{n}{5}

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