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Popular >

solvefor x,80=75-60cos(([pi*x])/(15))

Solution

solve for

x, 80 = 75 - 60 cos (\frac{[ π \cdot x ]}{15})

Solution

x = \frac{15 \cdot 1.65422 \dots}{π} + 30 n, x = - \frac{15 \cdot 1.65422 \dots}{π} + 30 n

Degrees

x = 452.54208 \dots^{\circ} + 1718.87338 \dots^{\circ} n, x = - 452.54208 \dots^{\circ} + 1718.87338 \dots^{\circ} n

Solution steps

80 = 75 - 60 cos (\frac{[ π x ]}{15})

Switch sides

75 - 60 cos (\frac{[ π x ]}{15}) = 80

Move

75

to the right side

75 - 60 cos (\frac{[ π x ]}{15}) = 80

Subtract

75

from both sides

75 - 60 cos (\frac{[ π x ]}{15}) - 75 = 80 - 75

Simplify

- 60 cos (\frac{[ π x ]}{15}) = 5

- 60 cos (\frac{[ π x ]}{15}) = 5

Divide both sides by

- 60

- 60 cos (\frac{[ π x ]}{15}) = 5

Divide both sides by

- 60

\frac{- 60 cos ( \frac{[ π x ]}{15} )}{- 60} = \frac{5}{- 60}

Simplify

\frac{- 60 cos ( \frac{[ π x ]}{15} )}{- 60} = \frac{5}{- 60}

Simplify

\frac{- 60 cos ( \frac{[ π x ]}{15} )}{- 60} : cos (\frac{[ π x ]}{15})

\frac{- 60 cos ( \frac{[ π x ]}{15} )}{- 60}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{60 cos ( \frac{[ π x ]}{15} )}{60}

Divide the numbers:

\frac{60}{60} = 1

= cos (\frac{[ π x ]}{15})

Simplify

\frac{5}{- 60} : - \frac{1}{12}

\frac{5}{- 60}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{5}{60}

Cancel the common factor:

5

= - \frac{1}{12}

cos (\frac{[ π x ]}{15}) = - \frac{1}{12}

cos (\frac{[ π x ]}{15}) = - \frac{1}{12}

cos (\frac{[ π x ]}{15}) = - \frac{1}{12}

Apply trig inverse properties

cos (\frac{[ π x ]}{15}) = - \frac{1}{12}

General solutions for

cos (\frac{[ π x ]}{15}) = - \frac{1}{12}

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

\frac{[ π x ]}{15} = arccos (- \frac{1}{12}) + 2 πn, \frac{[ π x ]}{15} = - arccos (- \frac{1}{12}) + 2 πn

\frac{[ π x ]}{15} = arccos (- \frac{1}{12}) + 2 πn, \frac{[ π x ]}{15} = - arccos (- \frac{1}{12}) + 2 πn

Solve

\frac{[ π x ]}{15} = arccos (- \frac{1}{12}) + 2 πn : x = \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

\frac{[ π x ]}{15} = arccos (- \frac{1}{12}) + 2 πn

Multiply both sides by

15

\frac{[ π x ]}{15} = arccos (- \frac{1}{12}) + 2 πn

Multiply both sides by

15

\frac{15 [ π x ]}{15} = 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Simplify

\frac{15 [ π x ]}{15} = 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Simplify

\frac{15 ( π x )}{15} : π x

\frac{15 [ π x ]}{15}

Remove parentheses:

(a) = a

= \frac{15 π x}{15}

Divide the numbers:

\frac{15}{15} = 1

= π x

Simplify

15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn : 15 arccos (- \frac{1}{12}) + 30 πn

15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Multiply the numbers:

15 \cdot 2 = 30

= 15 arccos (- \frac{1}{12}) + 30 πn

π x = 15 arccos (- \frac{1}{12}) + 30 πn

π x = 15 arccos (- \frac{1}{12}) + 30 πn

π x = 15 arccos (- \frac{1}{12}) + 30 πn

Divide both sides by

π

π x = 15 arccos (- \frac{1}{12}) + 30 πn

Divide both sides by

π

\frac{π x}{π} = \frac{15 arccos ( - \frac{1}{12} )}{π} + \frac{30 πn}{π}

Simplify

x = \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

x = \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

Solve

\frac{[ π x ]}{15} = - arccos (- \frac{1}{12}) + 2 πn : x = - \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

\frac{[ π x ]}{15} = - arccos (- \frac{1}{12}) + 2 πn

Multiply both sides by

15

\frac{[ π x ]}{15} = - arccos (- \frac{1}{12}) + 2 πn

Multiply both sides by

15

\frac{15 [ π x ]}{15} = - 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Simplify

\frac{15 [ π x ]}{15} = - 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Simplify

\frac{15 ( π x )}{15} : π x

\frac{15 [ π x ]}{15}

Remove parentheses:

(a) = a

= \frac{15 π x}{15}

Divide the numbers:

\frac{15}{15} = 1

= π x

Simplify

- 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn : - 15 arccos (- \frac{1}{12}) + 30 πn

- 15 arccos (- \frac{1}{12}) + 15 \cdot 2 πn

Multiply the numbers:

15 \cdot 2 = 30

= - 15 arccos (- \frac{1}{12}) + 30 πn

π x = - 15 arccos (- \frac{1}{12}) + 30 πn

π x = - 15 arccos (- \frac{1}{12}) + 30 πn

π x = - 15 arccos (- \frac{1}{12}) + 30 πn

Divide both sides by

π

π x = - 15 arccos (- \frac{1}{12}) + 30 πn

Divide both sides by

π

\frac{π x}{π} = - \frac{15 arccos ( - \frac{1}{12} )}{π} + \frac{30 πn}{π}

Simplify

x = - \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

x = - \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

x = \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n, x = - \frac{15 arccos ( - \frac{1}{12} )}{π} + 30 n

Show solutions in decimal form

x = \frac{15 \cdot 1.65422 \dots}{π} + 30 n, x = - \frac{15 \cdot 1.65422 \dots}{π} + 30 n

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