What is the general solution for cos(2x)= 3/5 ?

The general solution for cos(2x)= 3/5 is x=(0.92729…)/2+pin,x=pi-(0.92729…)/2+pin

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cos(2x)= 3/5

cos (2 x) = \frac{3}{5}

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

Degrees

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n, x = 153.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = \frac{3}{5}

Apply trig inverse properties

cos (2 x) = \frac{3}{5}

General solutions for

cos (2 x) = \frac{3}{5}

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

2 x = arccos (\frac{3}{5}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{5}) + 2 πn

2 x = arccos (\frac{3}{5}) + 2 πn, 2 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Solve

2 x = arccos (\frac{3}{5}) + 2 πn : x = \frac{arccos ( \frac{3}{5} )}{2} + πn

2 x = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{3}{5} )}{2} + πn

x = \frac{arccos ( \frac{3}{5} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{3}{5}) + 2 πn : x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

2 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

2 x = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

Simplify

x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

x = \frac{arccos ( \frac{3}{5} )}{2} + πn, x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

Show solutions in decimal form

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

- 4 cos (2 x) = 0

x, arcsin (y) = arcsin (x) + \frac{π}{3}

t, f = cos (b t)

3 cos (x) + sin (x) = 0

3 sec (2 x) = 2

What is the general solution for cos(2x)= 3/5 ?
The general solution for cos(2x)= 3/5 is x=(0.92729…)/2+pin,x=pi-(0.92729…)/2+pin