What is the general solution for cos(x/2)= 2/3 ?

The general solution for cos(x/2)= 2/3 is x=2*0.84106…+4pin,x=4pi-2*0.84106…+4pin

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cos(x/2)= 2/3

cos (\frac{x}{2}) = \frac{2}{3}

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

Degrees

x = 96.37937 \dots^{\circ} + 72 0^{\circ} n, x = 623.62062 \dots^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{x}{2}) = \frac{2}{3}

Apply trig inverse properties

cos (\frac{x}{2}) = \frac{2}{3}

General solutions for

cos (\frac{x}{2}) = \frac{2}{3}

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

\frac{x}{2} = arccos (\frac{2}{3}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{2}{3}) + 2 πn

\frac{x}{2} = arccos (\frac{2}{3}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

\frac{x}{2} = arccos (\frac{2}{3}) + 2 πn : x = 2 arccos (\frac{2}{3}) + 4 πn

\frac{x}{2} = arccos (\frac{2}{3}) + 2 πn

Multiply both sides by

2

\frac{x}{2} = arccos (\frac{2}{3}) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 arccos (\frac{2}{3}) + 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{2}{3}) + 2 \cdot 2 πn : 2 arccos (\frac{2}{3}) + 4 πn

2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn

Solve

\frac{x}{2} = 2 π - arccos (\frac{2}{3}) + 2 πn : x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

\frac{x}{2} = 2 π - arccos (\frac{2}{3}) + 2 πn

Multiply both sides by

2

\frac{x}{2} = 2 π - arccos (\frac{2}{3}) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 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{2}{3}) + 2 \cdot 2 πn : 4 π - 2 arccos (\frac{2}{3}) + 4 πn

2 \cdot 2 π - 2 arccos (\frac{2}{3}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn, x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

Show solutions in decimal form

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

cos (a) = \frac{7}{25}

\frac{sin ( x )}{1} + \frac{4}{sin ( x )} + 5 = 0

sin (x) = \frac{- 3}{13}

3 + 2 sin (2 x) = 23

\frac{1}{1 - cos ( θ )} - \frac{1}{1 + cos ( θ )} = 2 csc^{2} (θ)

What is the general solution for cos(x/2)= 2/3 ?
The general solution for cos(x/2)= 2/3 is x=2*0.84106…+4pin,x=4pi-2*0.84106…+4pin