What is the general solution for 6/pi =3cos(2x) ?

The general solution for 6/pi =3cos(2x) is x=(0.88068…)/2+pin,x=pi-(0.88068…)/2+pin

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6/pi =3cos(2x)

\frac{6}{π} = 3 cos (2 x)

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

Solution steps

\frac{6}{π} = 3 cos (2 x)

Switch sides

3 cos (2 x) = \frac{6}{π}

Divide both sides by

3

cos (2 x) = \frac{2}{π}

Apply trig inverse properties

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

Solve

2 x = 2 π - 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

sin (2 x) = - 2 cos (x)

4 - 8 cos^{2} (x) = 0

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

cos^{2} (x) - 4 cos (x) - 1 = 0

- 9 sin (3 x) = 0

What is the general solution for 6/pi =3cos(2x) ?
The general solution for 6/pi =3cos(2x) is x=(0.88068…)/2+pin,x=pi-(0.88068…)/2+pin