What is the general solution for 40cos((2pi)/3 t)-71=-80 ?

The general solution for 40cos((2pi)/3 t)-71=-80 is t=(3*1.79773…)/(2pi)+3n,t=-(3*1.79773…)/(2pi)+3n

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Popular Trigonometry >

40cos((2pi)/3 t)-71=-80

Solution

40 cos (\frac{2 π}{3} t) - 71 = - 80

Solution

t = \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n, t = - \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n

Degrees

t = 49.18025 \dots^{\circ} + 171.88733 \dots^{\circ} n, t = - 49.18025 \dots^{\circ} + 171.88733 \dots^{\circ} n

Solution steps

40 cos (\frac{2 π}{3} t) - 71 = - 80

Move

71

to the right side

40 cos (\frac{2 π}{3} t) - 71 = - 80

Add

71

to both sides

40 cos (\frac{2 π}{3} t) - 71 + 71 = - 80 + 71

Simplify

40 cos (\frac{2 π}{3} t) = - 9

40 cos (\frac{2 π}{3} t) = - 9

Divide both sides by

40

40 cos (\frac{2 π}{3} t) = - 9

Divide both sides by

40

\frac{40 cos ( \frac{2 π}{3} t )}{40} = \frac{- 9}{40}

Simplify

cos (\frac{2 π}{3} t) = - \frac{9}{40}

cos (\frac{2 π}{3} t) = - \frac{9}{40}

Apply trig inverse properties

cos (\frac{2 π}{3} t) = - \frac{9}{40}

General solutions for

cos (\frac{2 π}{3} t) = - \frac{9}{40}

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

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn, \frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn, \frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Solve

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn : t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn

Multiply both sides by

3

\frac{2 π}{3} t = arccos (- \frac{9}{40}) + 2 πn

Multiply both sides by

3

3 \cdot \frac{2 π}{3} t = 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplify

3 \cdot \frac{2 π}{3} t = 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplify

3 \cdot \frac{2 π}{3} t : 2 π t

3 \cdot \frac{2 π}{3} t

Multiply fractions:

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

= \frac{2 \cdot 3 π}{3} t

Cancel the common factor:

3

= t \cdot 2 π

Simplify

3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn : 3 arccos (- \frac{9}{40}) + 6 πn

3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

Divide both sides by

2 π

2 π t = 3 arccos (- \frac{9}{40}) + 6 πn

Divide both sides by

2 π

\frac{2 π t}{2 π} = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplify

\frac{2 π t}{2 π} = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplify

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π} : \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Cancel

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Cancel

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Divide the numbers:

\frac{6}{2} = 3

= \frac{3 πn}{π}

Cancel the common factor:

π

= 3 n

= 3 n

= \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

Solve

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn : t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Multiply both sides by

3

\frac{2 π}{3} t = - arccos (- \frac{9}{40}) + 2 πn

Multiply both sides by

3

3 \cdot \frac{2 π}{3} t = - 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplify

3 \cdot \frac{2 π}{3} t = - 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Simplify

3 \cdot \frac{2 π}{3} t : 2 π t

3 \cdot \frac{2 π}{3} t

Multiply fractions:

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

= \frac{2 \cdot 3 π}{3} t

Cancel the common factor:

3

= t \cdot 2 π

Simplify

- 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn : - 3 arccos (- \frac{9}{40}) + 6 πn

- 3 arccos (- \frac{9}{40}) + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

Divide both sides by

2 π

2 π t = - 3 arccos (- \frac{9}{40}) + 6 πn

Divide both sides by

2 π

\frac{2 π t}{2 π} = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplify

\frac{2 π t}{2 π} = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Simplify

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Divide the numbers:

\frac{2}{2} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

- \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π} : - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

- \frac{3 arccos ( - \frac{9}{40} )}{2 π} + \frac{6 πn}{2 π}

Cancel

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Cancel

\frac{6 πn}{2 π} : 3 n

\frac{6 πn}{2 π}

Divide the numbers:

\frac{6}{2} = 3

= \frac{3 πn}{π}

Cancel the common factor:

π

= 3 n

= 3 n

= - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

t = \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n, t = - \frac{3 arccos ( - \frac{9}{40} )}{2 π} + 3 n

Show solutions in decimal form

t = \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n, t = - \frac{3 \cdot 1.79773 \dots}{2 π} + 3 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 40cos((2pi)/3 t)-71=-80 ?
The general solution for 40cos((2pi)/3 t)-71=-80 is t=(3*1.79773…)/(2pi)+3n,t=-(3*1.79773…)/(2pi)+3n