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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Degrees

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

Solution steps

\frac{6}{π} = 3 cos (2 x)

Switch sides

3 cos (2 x) = \frac{6}{π}

Divide both sides by

3

3 cos (2 x) = \frac{6}{π}

Divide both sides by

3

\frac{3 cos ( 2 x )}{3} = \frac{\frac{6}{π}}{3}

Simplify

\frac{3 cos ( 2 x )}{3} = \frac{\frac{6}{π}}{3}

Simplify

\frac{3 cos ( 2 x )}{3} : cos (2 x)

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

Divide the numbers:

\frac{3}{3} = 1

= cos (2 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 (2 x) = \frac{2}{π}

cos (2 x) = \frac{2}{π}

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

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