What is the general solution for -2=(16)/pi cos(4*x) ?

The general solution for -2=(16)/pi cos(4*x) is x=(1.97436…)/4+(pin)/2 ,x=-(1.97436…)/4+(pin)/2

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Popular >

-2=(16)/pi cos(4*x)

Solution

- 2 = \frac{16}{π} cos (4 \cdot x)

Solution

x = \frac{1.97436 \dots}{4} + \frac{πn}{2}, x = - \frac{1.97436 \dots}{4} + \frac{πn}{2}

Degrees

x = 28.28063 \dots^{\circ} + 9 0^{\circ} n, x = - 28.28063 \dots^{\circ} + 9 0^{\circ} n

Solution steps

- 2 = \frac{16}{π} cos (4 x)

Switch sides

\frac{16}{π} cos (4 x) = - 2

Multiply both sides by

π

\frac{16}{π} cos (4 x) = - 2

Multiply both sides by

π

\frac{16}{π} cos (4 x) π = (- 2) π

Simplify

16 cos (4 x) = - 2 π

16 cos (4 x) = - 2 π

Divide both sides by

16

16 cos (4 x) = - 2 π

Divide both sides by

16

\frac{16 cos ( 4 x )}{16} = \frac{- 2 π}{16}

Simplify

\frac{16 cos ( 4 x )}{16} = \frac{- 2 π}{16}

Simplify

\frac{16 cos ( 4 x )}{16} : cos (4 x)

\frac{16 cos ( 4 x )}{16}

Divide the numbers:

\frac{16}{16} = 1

= cos (4 x)

Simplify

\frac{- 2 π}{16} : - \frac{π}{8}

\frac{- 2 π}{16}

Apply the fraction rule:

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

= - \frac{2 π}{16}

Cancel the common factor:

2

= - \frac{π}{8}

cos (4 x) = - \frac{π}{8}

cos (4 x) = - \frac{π}{8}

cos (4 x) = - \frac{π}{8}

Apply trig inverse properties

cos (4 x) = - \frac{π}{8}

General solutions for

cos (4 x) = - \frac{π}{8}

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

4 x = arccos (- \frac{π}{8}) + 2 πn, 4 x = - arccos (- \frac{π}{8}) + 2 πn

4 x = arccos (- \frac{π}{8}) + 2 πn, 4 x = - arccos (- \frac{π}{8}) + 2 πn

Solve

4 x = arccos (- \frac{π}{8}) + 2 πn : x = \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

4 x = arccos (- \frac{π}{8}) + 2 πn

Divide both sides by

4

4 x = arccos (- \frac{π}{8}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arccos ( - \frac{π}{8} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

x = \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

Solve

4 x = - arccos (- \frac{π}{8}) + 2 πn : x = - \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

4 x = - arccos (- \frac{π}{8}) + 2 πn

Divide both sides by

4

4 x = - arccos (- \frac{π}{8}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = - \frac{arccos ( - \frac{π}{8} )}{4} + \frac{2 πn}{4}

Simplify

x = - \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

x = - \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

x = \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}, x = - \frac{arccos ( - \frac{π}{8} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.97436 \dots}{4} + \frac{πn}{2}, x = - \frac{1.97436 \dots}{4} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for -2=(16)/pi cos(4*x) ?
The general solution for -2=(16)/pi cos(4*x) is x=(1.97436…)/4+(pin)/2 ,x=-(1.97436…)/4+(pin)/2