What is the general solution for 3cos((pix)/(12))+8.4=7 ?

The general solution for 3cos((pix)/(12))+8.4=7 is x=(12*2.05631…)/pi+24n,x=-(12*2.05631…)/pi+24n

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3cos((pix)/(12))+8.4=7

Solution

3 cos (\frac{π x}{12}) + 8.4 = 7

Solution

x = \frac{12 \cdot 2.05631 \dots}{π} + 24 n, x = - \frac{12 \cdot 2.05631 \dots}{π} + 24 n

Degrees

x = 450.03214 \dots^{\circ} + 1375.09870 \dots^{\circ} n, x = - 450.03214 \dots^{\circ} + 1375.09870 \dots^{\circ} n

Solution steps

3 cos (\frac{π x}{12}) + 8.4 = 7

Move

8.4

to the right side

3 cos (\frac{π x}{12}) + 8.4 = 7

Subtract

8.4

from both sides

3 cos (\frac{π x}{12}) + 8.4 - 8.4 = 7 - 8.4

Simplify

3 cos (\frac{π x}{12}) = - 1.4

3 cos (\frac{π x}{12}) = - 1.4

Divide both sides by

3

3 cos (\frac{π x}{12}) = - 1.4

Divide both sides by

3

\frac{3 cos ( \frac{π x}{12} )}{3} = \frac{- 1.4}{3}

Simplify

\frac{3 cos ( \frac{π x}{12} )}{3} = \frac{- 1.4}{3}

Simplify

\frac{3 cos ( \frac{π x}{12} )}{3} : cos (\frac{π x}{12})

\frac{3 cos ( \frac{π x}{12} )}{3}

Divide the numbers:

\frac{3}{3} = 1

= cos (\frac{π x}{12})

Simplify

\frac{- 1.4}{3} : - 0.46666 \dots

\frac{- 1.4}{3}

Apply the fraction rule:

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

= - \frac{1.4}{3}

Divide the numbers:

\frac{1.4}{3} = 0.46666 \dots

= - 0.46666 \dots

cos (\frac{π x}{12}) = - 0.46666 \dots

cos (\frac{π x}{12}) = - 0.46666 \dots

cos (\frac{π x}{12}) = - 0.46666 \dots

Apply trig inverse properties

cos (\frac{π x}{12}) = - 0.46666 \dots

General solutions for

cos (\frac{π x}{12}) = - 0.46666 \dots

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

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn, \frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn, \frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn

Solve

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn : x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn

Multiply both sides by

12

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn

Multiply both sides by

12

\frac{12 π x}{12} = 12 arccos (- 0.46666 \dots) + 12 \cdot 2 πn

Simplify

π x = 12 arccos (- 0.46666 \dots) + 24 πn

π x = 12 arccos (- 0.46666 \dots) + 24 πn

Divide both sides by

π

π x = 12 arccos (- 0.46666 \dots) + 24 πn

Divide both sides by

π

\frac{π x}{π} = \frac{12 arccos ( - 0.46666 \dots )}{π} + \frac{24 πn}{π}

Simplify

x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

Solve

\frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn : x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

\frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn

Multiply both sides by

12

\frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn

Multiply both sides by

12

\frac{12 π x}{12} = - 12 arccos (- 0.46666 \dots) + 12 \cdot 2 πn

Simplify

π x = - 12 arccos (- 0.46666 \dots) + 24 πn

π x = - 12 arccos (- 0.46666 \dots) + 24 πn

Divide both sides by

π

π x = - 12 arccos (- 0.46666 \dots) + 24 πn

Divide both sides by

π

\frac{π x}{π} = - \frac{12 arccos ( - 0.46666 \dots )}{π} + \frac{24 πn}{π}

Simplify

x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n, x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

Show solutions in decimal form

x = \frac{12 \cdot 2.05631 \dots}{π} + 24 n, x = - \frac{12 \cdot 2.05631 \dots}{π} + 24 n

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Frequently Asked Questions (FAQ)

What is the general solution for 3cos((pix)/(12))+8.4=7 ?
The general solution for 3cos((pix)/(12))+8.4=7 is x=(12*2.05631…)/pi+24n,x=-(12*2.05631…)/pi+24n