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)

solve for

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

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

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

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

Move

1

to the right side

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

Divide both sides by

- 1

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

Apply trig inverse properties

\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

Solve

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

cos (t) = sin (2 t)

2 cos^{2} (x) = 1 - cos^{2} (x)

4 + 2 cos (2 x) = 6 cos (x)

cos (x) - tan (x) cos (x) = 0

sin (θ) + cos (2 θ) = 0

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