What is the general solution for 10=7cos((pi/6)(t+6))+8 ?

The general solution for 10=7cos((pi/6)(t+6))+8 is t=(6*1.28104…)/pi+12n-6,t=12n+6-(6*1.28104…)/pi

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Popular Trigonometry >

10=7cos((pi/6)(t+6))+8

Solution

10 = 7 cos ((\frac{π}{6}) (t + 6)) + 8

Solution

t = \frac{6 \cdot 1.28104 \dots}{π} + 12 n - 6, t = 12 n + 6 - \frac{6 \cdot 1.28104 \dots}{π}

Degrees

t = - 203.59396 \dots^{\circ} + 687.54935 \dots^{\circ} n, t = 203.59396 \dots^{\circ} + 687.54935 \dots^{\circ} n

Solution steps

10 = 7 cos ((\frac{π}{6}) (t + 6)) + 8

Switch sides

7 cos (\frac{π}{6} (t + 6)) + 8 = 10

Move

8

to the right side

7 cos (\frac{π}{6} (t + 6)) + 8 = 10

Subtract

8

from both sides

7 cos (\frac{π}{6} (t + 6)) + 8 - 8 = 10 - 8

Simplify

7 cos (\frac{π}{6} (t + 6)) = 2

7 cos (\frac{π}{6} (t + 6)) = 2

Divide both sides by

7

7 cos (\frac{π}{6} (t + 6)) = 2

Divide both sides by

7

\frac{7 cos ( \frac{π}{6} ( t + 6 ) )}{7} = \frac{2}{7}

Simplify

cos (\frac{π}{6} (t + 6)) = \frac{2}{7}

cos (\frac{π}{6} (t + 6)) = \frac{2}{7}

Apply trig inverse properties

cos (\frac{π}{6} (t + 6)) = \frac{2}{7}

General solutions for

cos (\frac{π}{6} (t + 6)) = \frac{2}{7}

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

\frac{π}{6} (t + 6) = arccos (\frac{2}{7}) + 2 πn, \frac{π}{6} (t + 6) = 2 π - arccos (\frac{2}{7}) + 2 πn

\frac{π}{6} (t + 6) = arccos (\frac{2}{7}) + 2 πn, \frac{π}{6} (t + 6) = 2 π - arccos (\frac{2}{7}) + 2 πn

Solve

\frac{π}{6} (t + 6) = arccos (\frac{2}{7}) + 2 πn : t = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

\frac{π}{6} (t + 6) = arccos (\frac{2}{7}) + 2 πn

Multiply both sides by

6

\frac{π}{6} (t + 6) = arccos (\frac{2}{7}) + 2 πn

Multiply both sides by

6

6 \cdot \frac{π}{6} (t + 6) = 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (t + 6) = 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (t + 6) : π (t + 6)

6 \cdot \frac{π}{6} (t + 6)

Multiply fractions:

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

= \frac{6 π}{6} (t + 6)

Cancel the common factor:

6

= (t + 6) π

Simplify

6 arccos (\frac{2}{7}) + 6 \cdot 2 πn : 6 arccos (\frac{2}{7}) + 12 πn

6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 6 arccos (\frac{2}{7}) + 12 πn

Divide both sides by

π

π (t + 6) = 6 arccos (\frac{2}{7}) + 12 πn

Divide both sides by

π

\frac{π ( t + 6 )}{π} = \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π}

Simplify

t + 6 = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

t + 6 = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

Move

6

to the right side

t + 6 = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

Subtract

6

from both sides

t + 6 - 6 = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

Simplify

t = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

t = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

Solve

\frac{π}{6} (t + 6) = 2 π - arccos (\frac{2}{7}) + 2 πn : t = 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

\frac{π}{6} (t + 6) = 2 π - arccos (\frac{2}{7}) + 2 πn

Multiply both sides by

6

\frac{π}{6} (t + 6) = 2 π - arccos (\frac{2}{7}) + 2 πn

Multiply both sides by

6

6 \cdot \frac{π}{6} (t + 6) = 6 \cdot 2 π - 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (t + 6) = 6 \cdot 2 π - 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Simplify

6 \cdot \frac{π}{6} (t + 6) : π (t + 6)

6 \cdot \frac{π}{6} (t + 6)

Multiply fractions:

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

= \frac{6 π}{6} (t + 6)

Cancel the common factor:

6

= (t + 6) π

Simplify

6 \cdot 2 π - 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn : 12 π - 6 arccos (\frac{2}{7}) + 12 πn

6 \cdot 2 π - 6 arccos (\frac{2}{7}) + 6 \cdot 2 πn

Multiply the numbers:

6 \cdot 2 = 12

= 12 π - 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 12 π - 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 12 π - 6 arccos (\frac{2}{7}) + 12 πn

π (t + 6) = 12 π - 6 arccos (\frac{2}{7}) + 12 πn

Divide both sides by

π

π (t + 6) = 12 π - 6 arccos (\frac{2}{7}) + 12 πn

Divide both sides by

π

\frac{π ( t + 6 )}{π} = \frac{12 π}{π} - \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( t + 6 )}{π} = \frac{12 π}{π} - \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π}

Simplify

\frac{π ( t + 6 )}{π} : t + 6

\frac{π ( t + 6 )}{π}

Cancel the common factor:

π

= t + 6

Simplify

\frac{12 π}{π} - \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π} : 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

\frac{12 π}{π} - \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π}

Cancel

\frac{12 π}{π} : 12

\frac{12 π}{π}

Cancel the common factor:

π

= 12

= 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + \frac{12 πn}{π}

Cancel

\frac{12 πn}{π} : 12 n

\frac{12 πn}{π}

Cancel the common factor:

π

= 12 n

= 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

t + 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

t + 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

t + 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

Move

6

to the right side

t + 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n

Subtract

6

from both sides

t + 6 - 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

Simplify

t + 6 - 6 = 12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

Simplify

t + 6 - 6 : t

t + 6 - 6

Add similar elements:

6 - 6 = 0

= t

Simplify

12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6 : 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

12 - \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6

Subtract the numbers:

12 - 6 = 6

= 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

t = 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

t = 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

t = 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

t = \frac{6 arccos ( \frac{2}{7} )}{π} + 12 n - 6, t = 12 n + 6 - \frac{6 arccos ( \frac{2}{7} )}{π}

Show solutions in decimal form

t = \frac{6 \cdot 1.28104 \dots}{π} + 12 n - 6, t = 12 n + 6 - \frac{6 \cdot 1.28104 \dots}{π}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 10=7cos((pi/6)(t+6))+8 ?
The general solution for 10=7cos((pi/6)(t+6))+8 is t=(6*1.28104…)/pi+12n-6,t=12n+6-(6*1.28104…)/pi