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

The general solution for cos(2x)= 2/pi is x=(0.88068…)/2+pin,x=pi-(0.88068…)/2+pin

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cos(2x)= 2/pi

cos (2 x) = \frac{2}{π}

x = \frac{0.88068 \dots}{2} + πn, x = π - \frac{0.88068 \dots}{2} + πn

Degrees

x = 25.22988 \dots^{\circ} + 18 0^{\circ} n, x = 154.77011 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) = \frac{2}{π}

Apply trig inverse properties

cos (2 x) = \frac{2}{π}

General solutions for

cos (2 x) = \frac{2}{π}

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

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

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

Solve

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

2 x = arccos (\frac{2}{π}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{2}{π}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.88068 \dots}{2} + πn, x = π - \frac{0.88068 \dots}{2} + πn

4 tan^{2} (x) + 8 sec (x) = 1

cos^{2} (θ) + sin (θ) = 2

3 tan^{2} (θ) + tan (θ) = 0

6 sin (θ) + 1 = 4 sin (θ)

tan (t) = - \frac{1}{3}

What is the general solution for cos(2x)= 2/pi ?
The general solution for cos(2x)= 2/pi is x=(0.88068…)/2+pin,x=pi-(0.88068…)/2+pin