What is the general solution for solvefor k,1.5=6(-cos(k/2)+1) ?

The general solution for solvefor k,1.5=6(-cos(k/2)+1) is k=2*0.72273…+4pin,k=4pi-2*0.72273…+4pin

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solvefor k,1.5=6(-cos(k/2)+1)

Solution

solve for

k, 1.5 = 6 (- cos (\frac{k}{2}) + 1)

Solution

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

Degrees

k = 82.81924 \dots^{\circ} + 72 0^{\circ} n, k = 637.18075 \dots^{\circ} + 72 0^{\circ} n

Solution steps

1.5 = 6 (- cos (\frac{k}{2}) + 1)

Switch sides

6 (- cos (\frac{k}{2}) + 1) = 1.5

Divide both sides by

6

6 (- cos (\frac{k}{2}) + 1) = 1.5

Divide both sides by

6

\frac{6 ( - cos ( \frac{k}{2} ) + 1 )}{6} = \frac{1.5}{6}

Simplify

- cos (\frac{k}{2}) + 1 = 0.25

- cos (\frac{k}{2}) + 1 = 0.25

Move

1

to the right side

- cos (\frac{k}{2}) + 1 = 0.25

Subtract

1

from both sides

- cos (\frac{k}{2}) + 1 - 1 = 0.25 - 1

Simplify

- cos (\frac{k}{2}) = - 0.75

- cos (\frac{k}{2}) = - 0.75

Divide both sides by

- 1

- cos (\frac{k}{2}) = - 0.75

Divide both sides by

- 1

\frac{- cos ( \frac{k}{2} )}{- 1} = \frac{- 0.75}{- 1}

Simplify

cos (\frac{k}{2}) = 0.75

cos (\frac{k}{2}) = 0.75

Apply trig inverse properties

cos (\frac{k}{2}) = 0.75

General solutions for

cos (\frac{k}{2}) = 0.75

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

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

\frac{k}{2} = arccos (0.75) + 2 πn, \frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Solve

\frac{k}{2} = arccos (0.75) + 2 πn : k = 2 arccos (0.75) + 4 πn

\frac{k}{2} = arccos (0.75) + 2 πn

Multiply both sides by

2

\frac{k}{2} = arccos (0.75) + 2 πn

Multiply both sides by

2

\frac{2 k}{2} = 2 arccos (0.75) + 2 \cdot 2 πn

Simplify

k = 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn

Solve

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn : k = 4 π - 2 arccos (0.75) + 4 πn

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Multiply both sides by

2

\frac{k}{2} = 2 π - arccos (0.75) + 2 πn

Multiply both sides by

2

\frac{2 k}{2} = 2 \cdot 2 π - 2 arccos (0.75) + 2 \cdot 2 πn

Simplify

k = 4 π - 2 arccos (0.75) + 4 πn

k = 4 π - 2 arccos (0.75) + 4 πn

k = 2 arccos (0.75) + 4 πn, k = 4 π - 2 arccos (0.75) + 4 πn

Show solutions in decimal form

k = 2 \cdot 0.72273 \dots + 4 πn, k = 4 π - 2 \cdot 0.72273 \dots + 4 πn

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor k,1.5=6(-cos(k/2)+1) ?
The general solution for solvefor k,1.5=6(-cos(k/2)+1) is k=2*0.72273…+4pin,k=4pi-2*0.72273…+4pin