What is the general solution for 0.8= 1/2 (1-cos(θ/2)) ?

The general solution for 0.8= 1/2 (1-cos(θ/2)) is θ=2*2.21429…+4pin,θ=-2*2.21429…+4pin

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0.8= 1/2 (1-cos(θ/2))

0.8 = \frac{1}{2} (1 - cos (\frac{θ}{2}))

θ = 2 \cdot 2.21429 \dots + 4 πn, θ = - 2 \cdot 2.21429 \dots + 4 πn

Solution steps

0.8 = \frac{1}{2} (1 - cos (\frac{θ}{2}))

Switch sides

\frac{1}{2} (1 - cos (\frac{θ}{2})) = 0.8

Multiply both sides by

2

1 - cos (\frac{θ}{2}) = 1.6

Move

1

to the right side

- cos (\frac{θ}{2}) = 0.6

Divide both sides by

- 1

cos (\frac{θ}{2}) = - 0.6

Apply trig inverse properties

\frac{θ}{2} = arccos (- 0.6) + 2 πn, \frac{θ}{2} = - arccos (- 0.6) + 2 πn

Solve

\frac{θ}{2} = arccos (- 0.6) + 2 πn : θ = 2 arccos (- 0.6) + 4 πn

Solve

\frac{θ}{2} = - arccos (- 0.6) + 2 πn : θ = - 2 arccos (- 0.6) + 4 πn

θ = 2 arccos (- 0.6) + 4 πn, θ = - 2 arccos (- 0.6) + 4 πn

Show solutions in decimal form

θ = 2 \cdot 2.21429 \dots + 4 πn, θ = - 2 \cdot 2.21429 \dots + 4 πn

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

3 sec (θ) + 1 = 7, 0 \leq θ < 2 π

sin (A) cos (A) = sin (A)

tan (\frac{x}{2} - \frac{π}{4}) = 1

3 sin (θ) = 1

What is the general solution for 0.8= 1/2 (1-cos(θ/2)) ?
The general solution for 0.8= 1/2 (1-cos(θ/2)) is θ=2*2.21429…+4pin,θ=-2*2.21429…+4pin