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

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

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3cos(x)= 6/pi

3 cos (x) = \frac{6}{π}

x = 0.88068 \dots + 2 πn, x = 2 π - 0.88068 \dots + 2 πn

Degrees

x = 50.45977 \dots^{\circ} + 36 0^{\circ} n, x = 309.54022 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) = \frac{6}{π}

Divide both sides by

3

3 cos (x) = \frac{6}{π}

Divide both sides by

3

\frac{3 cos ( x )}{3} = \frac{\frac{6}{π}}{3}

Simplify

\frac{3 cos ( x )}{3} = \frac{\frac{6}{π}}{3}

Simplify

\frac{3 cos ( x )}{3} : cos (x)

\frac{3 cos ( x )}{3}

Divide the numbers:

\frac{3}{3} = 1

= cos (x)

Simplify

\frac{\frac{6}{π}}{3} : \frac{2}{π}

\frac{\frac{6}{π}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{6}{π 3}

Divide the numbers:

\frac{6}{3} = 2

= \frac{2}{π}

cos (x) = \frac{2}{π}

cos (x) = \frac{2}{π}

cos (x) = \frac{2}{π}

Apply trig inverse properties

cos (x) = \frac{2}{π}

General solutions for

cos (x) = \frac{2}{π}

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

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

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

Show solutions in decimal form

x = 0.88068 \dots + 2 πn, x = 2 π - 0.88068 \dots + 2 πn

6 cos (2 θ) = 18 cos (θ) - 12

cos (\frac{2}{3} x - \frac{π}{2}) = 1

tan^{2} (x) sin (x) = sin (x), 0 \leq x \leq 2 π

- 3 sin (t) = 0

x, 0 = cos (x) - sin (x)

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