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

Degrees

x = 67.11461 \dots^{\circ} + 72 0^{\circ} n, x = 652.88538 \dots^{\circ} + 72 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

\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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arccos (\frac{5}{6}) + 4 πn

x = 2 arccos (\frac{5}{6}) + 4 πn

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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

2 \cdot 2 π - 2 arccos (\frac{5}{6}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 π - 2 arccos (\frac{5}{6}) + 4 πn

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

x = 4 π - 2 arccos (\frac{5}{6}) + 4 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