What is the general solution for 1.5=1+0.6cos((pit)/2) ?

The general solution for 1.5=1+0.6cos((pit)/2) is t=(2*0.58568…)/pi+4n,t=4-(2*0.58568…)/pi+4n

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Popular Trigonometry >

1.5=1+0.6cos((pit)/2)

Solution

1.5 = 1 + 0.6 cos (\frac{π t}{2})

Solution

t = \frac{2 \cdot 0.58568 \dots}{π} + 4 n, t = 4 - \frac{2 \cdot 0.58568 \dots}{π} + 4 n

Degrees

t = 21.36324 \dots^{\circ} + 229.18311 \dots^{\circ} n, t = 207.81987 \dots^{\circ} + 229.18311 \dots^{\circ} n

Solution steps

1.5 = 1 + 0.6 cos (\frac{π t}{2})

Switch sides

1 + 0.6 cos (\frac{π t}{2}) = 1.5

Multiply both sides by

10

1 + 0.6 cos (\frac{π t}{2}) = 1.5

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

1 \cdot 10 + 0.6 cos (\frac{π t}{2}) \cdot 10 = 1.5 \cdot 10

Refine

10 + 6 cos (\frac{π t}{2}) = 15

10 + 6 cos (\frac{π t}{2}) = 15

Move

10

to the right side

10 + 6 cos (\frac{π t}{2}) = 15

Subtract

10

from both sides

10 + 6 cos (\frac{π t}{2}) - 10 = 15 - 10

Simplify

6 cos (\frac{π t}{2}) = 5

6 cos (\frac{π t}{2}) = 5

Divide both sides by

6

6 cos (\frac{π t}{2}) = 5

Divide both sides by

6

\frac{6 cos ( \frac{π t}{2} )}{6} = \frac{5}{6}

Simplify

cos (\frac{π t}{2}) = \frac{5}{6}

cos (\frac{π t}{2}) = \frac{5}{6}

Apply trig inverse properties

cos (\frac{π t}{2}) = \frac{5}{6}

General solutions for

cos (\frac{π t}{2}) = \frac{5}{6}

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

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn : t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn

Multiply both sides by

2

\frac{π t}{2} = arccos (\frac{5}{6}) + 2 πn

Multiply both sides by

2

\frac{2 π t}{2} = 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Simplify

\frac{2 π t}{2} = 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Simplify

\frac{2 π t}{2} : π t

\frac{2 π t}{2}

Divide the numbers:

\frac{2}{2} = 1

= π t

Simplify

2 arccos (\frac{5}{6}) + 2 \cdot 2 πn : 2 arccos (\frac{5}{6}) + 4 πn

2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arccos (\frac{5}{6}) + 4 πn

π t = 2 arccos (\frac{5}{6}) + 4 πn

π t = 2 arccos (\frac{5}{6}) + 4 πn

π t = 2 arccos (\frac{5}{6}) + 4 πn

Divide both sides by

π

π t = 2 arccos (\frac{5}{6}) + 4 πn

Divide both sides by

π

\frac{π t}{π} = \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π}

Simplify

t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

Solve

\frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn : t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

\frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

Multiply both sides by

2

\frac{π t}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

Multiply both sides by

2

\frac{2 π t}{2} = 2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Simplify

\frac{2 π t}{2} = 2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Simplify

\frac{2 π t}{2} : π t

\frac{2 π t}{2}

Divide the numbers:

\frac{2}{2} = 1

= π t

Simplify

2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{5}{6}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{5}{6}) + 4 πn

π t = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

π t = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

π t = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

Divide both sides by

π

π t = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

Divide both sides by

π

\frac{π t}{π} = \frac{4 π}{π} - \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π}

Simplify

\frac{π t}{π} = \frac{4 π}{π} - \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π}

Simplify

\frac{π t}{π} : t

\frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{4 π}{π} - \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π} : 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

\frac{4 π}{π} - \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π}

Cancel

\frac{4 π}{π} : 4

\frac{4 π}{π}

Cancel the common factor:

π

= 4

= 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + \frac{4 πn}{π}

Cancel

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

t = \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n, t = 4 - \frac{2 arccos ( \frac{5}{6} )}{π} + 4 n

Show solutions in decimal form

t = \frac{2 \cdot 0.58568 \dots}{π} + 4 n, t = 4 - \frac{2 \cdot 0.58568 \dots}{π} + 4 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 1.5=1+0.6cos((pit)/2) ?
The general solution for 1.5=1+0.6cos((pit)/2) is t=(2*0.58568…)/pi+4n,t=4-(2*0.58568…)/pi+4n