What is the general solution for 960=480(1-cos(7.5x)) ?

The general solution for 960=480(1-cos(7.5x)) is x=(2pi)/(15)+(4pin)/(15)

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960=480(1-cos(7.5x))

Solution

960 = 480 (1 - cos (7.5 x))

Solution

x = \frac{2 π}{15} + \frac{4 πn}{15}

Degrees

x = 2 4^{\circ} + 4 8^{\circ} n

Solution steps

960 = 480 (1 - cos (7.5 x))

Switch sides

480 (1 - cos (7.5 x)) = 960

Divide both sides by

480

480 (1 - cos (7.5 x)) = 960

Divide both sides by

480

\frac{480 ( 1 - cos ( 7.5 x ) )}{480} = \frac{960}{480}

Simplify

1 - cos (7.5 x) = 2

1 - cos (7.5 x) = 2

Move

1

to the right side

1 - cos (7.5 x) = 2

Subtract

1

from both sides

1 - cos (7.5 x) - 1 = 2 - 1

Simplify

- cos (7.5 x) = 1

- cos (7.5 x) = 1

Divide both sides by

- 1

- cos (7.5 x) = 1

Divide both sides by

- 1

\frac{- cos ( 7.5 x )}{- 1} = \frac{1}{- 1}

Simplify

cos (7.5 x) = - 1

cos (7.5 x) = - 1

General solutions for

cos (7.5 x) = - 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

7.5 x = π + 2 πn

7.5 x = π + 2 πn

Solve

7.5 x = π + 2 πn : x = \frac{2 π}{15} + \frac{4 πn}{15}

7.5 x = π + 2 πn

Multiply both sides by

10

7.5 x = π + 2 πn

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

7.5 x \cdot 10 = π 10 + 2 πn \cdot 10

Refine

75 x = 10 π + 20 πn

75 x = 10 π + 20 πn

Divide both sides by

75

75 x = 10 π + 20 πn

Divide both sides by

75

\frac{75 x}{75} = \frac{10 π}{75} + \frac{20 πn}{75}

Simplify

\frac{75 x}{75} = \frac{10 π}{75} + \frac{20 πn}{75}

Simplify

\frac{75 x}{75} : x

\frac{75 x}{75}

Divide the numbers:

\frac{75}{75} = 1

= x

Simplify

\frac{10 π}{75} + \frac{20 πn}{75} : \frac{2 π}{15} + \frac{4 πn}{15}

\frac{10 π}{75} + \frac{20 πn}{75}

Cancel

\frac{10 π}{75} : \frac{2 π}{15}

\frac{10 π}{75}

Cancel the common factor:

5

= \frac{2 π}{15}

= \frac{2 π}{15} + \frac{20 πn}{75}

Cancel

\frac{20 πn}{75} : \frac{4 πn}{15}

\frac{20 πn}{75}

Cancel the common factor:

5

= \frac{4 πn}{15}

= \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

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Frequently Asked Questions (FAQ)

What is the general solution for 960=480(1-cos(7.5x)) ?
The general solution for 960=480(1-cos(7.5x)) is x=(2pi)/(15)+(4pin)/(15)