What is the general solution for cos(2x)= 4/5 ?

The general solution for cos(2x)= 4/5 is x=(0.64350…)/2+pin,x=pi-(0.64350…)/2+pin

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cos(2x)= 4/5

cos (2 x) = \frac{4}{5}

x = \frac{0.64350 \dots}{2} + πn, x = π - \frac{0.64350 \dots}{2} + πn

Degrees

x = 18.43494 \dots^{\circ} + 18 0^{\circ} n, x = 161.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = \frac{4}{5}

Apply trig inverse properties

cos (2 x) = \frac{4}{5}

General solutions for

cos (2 x) = \frac{4}{5}

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

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

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

Solve

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

2 x = arccos (\frac{4}{5}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{4}{5}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.64350 \dots}{2} + πn, x = π - \frac{0.64350 \dots}{2} + πn

tan (x) = \frac{160}{85}

sin (x) a = π

sin (5 x) + sin (x) = 0

cot^{2} (x) + csc^{2} (x) = 3

2 tan (x) = 0

What is the general solution for cos(2x)= 4/5 ?
The general solution for cos(2x)= 4/5 is x=(0.64350…)/2+pin,x=pi-(0.64350…)/2+pin