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Popular Trigonometry >

21cos((2pi)/(687)t)+228=220

Solution

21 cos (\frac{2 π}{687} t) + 228 = 220

Solution

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

Degrees

t = 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n, t = - 12288.95420 \dots^{\circ} + 39362.20052 \dots^{\circ} n

Solution steps

21 cos (\frac{2 π}{687} t) + 228 = 220

Move

228

to the right side

21 cos (\frac{2 π}{687} t) + 228 = 220

Subtract

228

from both sides

21 cos (\frac{2 π}{687} t) + 228 - 228 = 220 - 228

Simplify

21 cos (\frac{2 π}{687} t) = - 8

21 cos (\frac{2 π}{687} t) = - 8

Divide both sides by

21

21 cos (\frac{2 π}{687} t) = - 8

Divide both sides by

21

\frac{21 cos ( \frac{2 π}{687} t )}{21} = \frac{- 8}{21}

Simplify

cos (\frac{2 π}{687} t) = - \frac{8}{21}

cos (\frac{2 π}{687} t) = - \frac{8}{21}

Apply trig inverse properties

cos (\frac{2 π}{687} t) = - \frac{8}{21}

General solutions for

cos (\frac{2 π}{687} t) = - \frac{8}{21}

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

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn, \frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Solve

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn : t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

Multiply both sides by

687

\frac{2 π}{687} t = arccos (- \frac{8}{21}) + 2 πn

Multiply both sides by

687

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplify

687 \cdot \frac{2 π}{687} t = 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplify

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

Multiply fractions:

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

= \frac{2 \cdot 687 π}{687} t

Cancel the common factor:

687

= t \cdot 2 π

Simplify

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : 687 arccos (- \frac{8}{21}) + 1374 πn

687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Multiply the numbers:

687 \cdot 2 = 1374

= 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

Divide both sides by

2 π

2 π t = 687 arccos (- \frac{8}{21}) + 1374 πn

Divide both sides by

2 π

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplify

\frac{2 π t}{2 π} = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplify

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Cancel

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Cancel

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Divide the numbers:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

Cancel the common factor:

π

= 687 n

= 687 n

= \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

Solve

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn : t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Multiply both sides by

687

\frac{2 π}{687} t = - arccos (- \frac{8}{21}) + 2 πn

Multiply both sides by

687

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplify

687 \cdot \frac{2 π}{687} t = - 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Simplify

687 \cdot \frac{2 π}{687} t : 2 π t

687 \cdot \frac{2 π}{687} t

Multiply fractions:

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

= \frac{2 \cdot 687 π}{687} t

Cancel the common factor:

687

= t \cdot 2 π

Simplify

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn : - 687 arccos (- \frac{8}{21}) + 1374 πn

- 687 arccos (- \frac{8}{21}) + 687 \cdot 2 πn

Multiply the numbers:

687 \cdot 2 = 1374

= - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

Divide both sides by

2 π

2 π t = - 687 arccos (- \frac{8}{21}) + 1374 πn

Divide both sides by

2 π

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplify

\frac{2 π t}{2 π} = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Simplify

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

- \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π} : - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

- \frac{687 arccos ( - \frac{8}{21} )}{2 π} + \frac{1374 πn}{2 π}

Cancel

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Cancel

\frac{1374 πn}{2 π} : 687 n

\frac{1374 πn}{2 π}

Divide the numbers:

\frac{1374}{2} = 687

= \frac{687 πn}{π}

Cancel the common factor:

π

= 687 n

= 687 n

= - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

t = \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n, t = - \frac{687 arccos ( - \frac{8}{21} )}{2 π} + 687 n

Show solutions in decimal form

t = \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n, t = - \frac{687 \cdot 1.96162 \dots}{2 π} + 687 n

Graph

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