What is the general solution for cos(x/2)= 5/6 ?

The general solution for cos(x/2)= 5/6 is x=2*0.58568…+4pin,x=4pi-2*0.58568…+4pin

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cos(x/2)= 5/6

cos (\frac{x}{2}) = \frac{5}{6}

x = 2 \cdot 0.58568 \dots + 4 πn, x = 4 π - 2 \cdot 0.58568 \dots + 4 πn

Solution steps

cos (\frac{x}{2}) = \frac{5}{6}

Apply trig inverse properties

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn, \frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

\frac{x}{2} = arccos (\frac{5}{6}) + 2 πn : x = 2 arccos (\frac{5}{6}) + 4 πn

Solve

\frac{x}{2} = 2 π - arccos (\frac{5}{6}) + 2 πn : x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn, x = 4 π - 2 arccos (\frac{5}{6}) + 4 πn

Show solutions in decimal form

x = 2 \cdot 0.58568 \dots + 4 πn, x = 4 π - 2 \cdot 0.58568 \dots + 4 πn

sin (B) = \frac{9}{16}

4 5^{\circ} = 57. 7^{\circ} + arctan (\frac{3.5}{x}) - arctan (\frac{175}{x})

\frac{1}{2} - cos (\frac{x}{2}) = 0

tan (θ) = \frac{2 π}{3}

2 sin (5 x) = 1

What is the general solution for cos(x/2)= 5/6 ?
The general solution for cos(x/2)= 5/6 is x=2*0.58568…+4pin,x=4pi-2*0.58568…+4pin