What is the general solution for 21=24+8cos((pix)/6) ?

The general solution for 21=24+8cos((pix)/6) is x=(6*1.95519…)/pi+12n,x=-(6*1.95519…)/pi+12n

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Popular Trigonometry >

21=24+8cos((pix)/6)

Solution

21 = 24 + 8 cos (\frac{π x}{6})

Solution

x = \frac{6 \cdot 1.95519 \dots}{π} + 12 n, x = - \frac{6 \cdot 1.95519 \dots}{π} + 12 n

Degrees

x = 213.95067 \dots^{\circ} + 687.54935 \dots^{\circ} n, x = - 213.95067 \dots^{\circ} + 687.54935 \dots^{\circ} n

Solution steps

21 = 24 + 8 cos (\frac{π x}{6})

Switch sides

24 + 8 cos (\frac{π x}{6}) = 21

Move

24

to the right side

24 + 8 cos (\frac{π x}{6}) = 21

Subtract

24

from both sides

24 + 8 cos (\frac{π x}{6}) - 24 = 21 - 24

Simplify

8 cos (\frac{π x}{6}) = - 3

8 cos (\frac{π x}{6}) = - 3

Divide both sides by

8

8 cos (\frac{π x}{6}) = - 3

Divide both sides by

8

\frac{8 cos ( \frac{π x}{6} )}{8} = \frac{- 3}{8}

Simplify

cos (\frac{π x}{6}) = - \frac{3}{8}

cos (\frac{π x}{6}) = - \frac{3}{8}

Apply trig inverse properties

cos (\frac{π x}{6}) = - \frac{3}{8}

General solutions for

cos (\frac{π x}{6}) = - \frac{3}{8}

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

\frac{π x}{6} = arccos (- \frac{3}{8}) + 2 πn, \frac{π x}{6} = - arccos (- \frac{3}{8}) + 2 πn

\frac{π x}{6} = arccos (- \frac{3}{8}) + 2 πn, \frac{π x}{6} = - arccos (- \frac{3}{8}) + 2 πn

Solve

\frac{π x}{6} = arccos (- \frac{3}{8}) + 2 πn : x = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

\frac{π x}{6} = arccos (- \frac{3}{8}) + 2 πn

Multiply both sides by

6

\frac{π x}{6} = arccos (- \frac{3}{8}) + 2 πn

Multiply both sides by

6

\frac{6 π x}{6} = 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplify

\frac{6 π x}{6} = 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplify

\frac{6 π x}{6} : π x

\frac{6 π x}{6}

Divide the numbers:

\frac{6}{6} = 1

= π x

Simplify

6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn : 6 arccos (- \frac{3}{8}) + 12 πn

6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 6 arccos (- \frac{3}{8}) + 12 πn

π x = 6 arccos (- \frac{3}{8}) + 12 πn

π x = 6 arccos (- \frac{3}{8}) + 12 πn

π x = 6 arccos (- \frac{3}{8}) + 12 πn

Divide both sides by

π

π x = 6 arccos (- \frac{3}{8}) + 12 πn

Divide both sides by

π

\frac{π x}{π} = \frac{6 arccos ( - \frac{3}{8} )}{π} + \frac{12 πn}{π}

Simplify

x = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

x = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

Solve

\frac{π x}{6} = - arccos (- \frac{3}{8}) + 2 πn : x = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

\frac{π x}{6} = - arccos (- \frac{3}{8}) + 2 πn

Multiply both sides by

6

\frac{π x}{6} = - arccos (- \frac{3}{8}) + 2 πn

Multiply both sides by

6

\frac{6 π x}{6} = - 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplify

\frac{6 π x}{6} = - 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Simplify

\frac{6 π x}{6} : π x

\frac{6 π x}{6}

Divide the numbers:

\frac{6}{6} = 1

= π x

Simplify

- 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn : - 6 arccos (- \frac{3}{8}) + 12 πn

- 6 arccos (- \frac{3}{8}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= - 6 arccos (- \frac{3}{8}) + 12 πn

π x = - 6 arccos (- \frac{3}{8}) + 12 πn

π x = - 6 arccos (- \frac{3}{8}) + 12 πn

π x = - 6 arccos (- \frac{3}{8}) + 12 πn

Divide both sides by

π

π x = - 6 arccos (- \frac{3}{8}) + 12 πn

Divide both sides by

π

\frac{π x}{π} = - \frac{6 arccos ( - \frac{3}{8} )}{π} + \frac{12 πn}{π}

Simplify

x = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

x = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

x = \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n, x = - \frac{6 arccos ( - \frac{3}{8} )}{π} + 12 n

Show solutions in decimal form

x = \frac{6 \cdot 1.95519 \dots}{π} + 12 n, x = - \frac{6 \cdot 1.95519 \dots}{π} + 12 n

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the general solution for 21=24+8cos((pix)/6) ?
The general solution for 21=24+8cos((pix)/6) is x=(6*1.95519…)/pi+12n,x=-(6*1.95519…)/pi+12n