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

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

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

solve for

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

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

Solution steps

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

tan (x) sec (x) = 2 tan (x)

tan (x) = \frac{5.1}{10.5}

tan (x) = 3, 0 \leq x < 2 π

3 tan^{2} (x) + 4 tan (x) - 3 = 0

sin (2 x) = 3 cos (x), 0 \leq x \leq 2 π

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