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

Degrees

x = 151.04497 \dots^{\circ} + 72 0^{\circ} n, x = 568.95502 \dots^{\circ} + 72 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

\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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

2 arccos (\frac{1}{4}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arccos (\frac{1}{4}) + 4 πn

x = 2 arccos (\frac{1}{4}) + 4 πn

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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

2 \cdot 2 π - 2 arccos (\frac{1}{4}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{1}{4}) + 4 πn

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

x = 4 π - 2 arccos (\frac{1}{4}) + 4 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