What is the general solution for cos(x/2)= 1/4 ?

The general solution for cos(x/2)= 1/4 is x=2*1.31811…+4pin,x=4pi-2*1.31811…+4pin

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cos(x/2)= 1/4

cos (\frac{x}{2}) = \frac{1}{4}

x = 2 \cdot 1.31811 \dots + 4 πn, x = 4 π - 2 \cdot 1.31811 \dots + 4 πn

Solution steps

cos (\frac{x}{2}) = \frac{1}{4}

Apply trig inverse properties

\frac{x}{2} = arccos (\frac{1}{4}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

\frac{x}{2} = arccos (\frac{1}{4}) + 2 πn : x = 2 arccos (\frac{1}{4}) + 4 πn

Solve

\frac{x}{2} = 2 π - arccos (\frac{1}{4}) + 2 πn : x = 4 π - 2 arccos (\frac{1}{4}) + 4 πn

x = 2 arccos (\frac{1}{4}) + 4 πn, x = 4 π - 2 arccos (\frac{1}{4}) + 4 πn

Show solutions in decimal form

x = 2 \cdot 1.31811 \dots + 4 πn, x = 4 π - 2 \cdot 1.31811 \dots + 4 πn

x, y = 2 arcsin (x - 1)

x, - 2 sin (x) - 1 = 0

sin (t) = \frac{1}{8}

sin (θ) - 0.2 \cdot cos (θ) = 0.48979

1 = 1 + 3 sin (3 θ)

What is the general solution for cos(x/2)= 1/4 ?
The general solution for cos(x/2)= 1/4 is x=2*1.31811…+4pin,x=4pi-2*1.31811…+4pin