What is the general solution for 8cos(6x)=2 ?

The general solution for 8cos(6x)=2 is x=(1.31811…)/6+(pin)/3 ,x= pi/3-(1.31811…)/6+(pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

8cos(6x)=2

Solution

8 cos (6 x) = 2

Solution

x = \frac{1.31811 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.31811 \dots}{6} + \frac{πn}{3}

Degrees

x = 12.58708 \dots^{\circ} + 6 0^{\circ} n, x = 47.41291 \dots^{\circ} + 6 0^{\circ} n

Solution steps

8 cos (6 x) = 2

Divide both sides by

8

8 cos (6 x) = 2

Divide both sides by

8

\frac{8 cos ( 6 x )}{8} = \frac{2}{8}

Simplify

cos (6 x) = \frac{1}{4}

cos (6 x) = \frac{1}{4}

Apply trig inverse properties

cos (6 x) = \frac{1}{4}

General solutions for

cos (6 x) = \frac{1}{4}

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

6 x = arccos (\frac{1}{4}) + 2 πn, 6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

6 x = arccos (\frac{1}{4}) + 2 πn, 6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

6 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{1}{4}) + 2 πn

Divide both sides by

6

6 x = arccos (\frac{1}{4}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

Simplify

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

Solve

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Divide both sides by

6

6 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

Simplify

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

Simplify

\frac{6 x}{6} : x

\frac{6 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= x

Simplify

\frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

Cancel

\frac{2 π}{6} : \frac{π}{3}

\frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{2 πn}{6}

Cancel

\frac{2 πn}{6} : \frac{πn}{3}

\frac{2 πn}{6}

Cancel the common factor:

2

= \frac{πn}{3}

= \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{1}{4} )}{6} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{1.31811 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.31811 \dots}{6} + \frac{πn}{3}

Graph

Popular Examples

sin(x)=(-(6))/((7)cos(x))

5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A))

2+2sin(θ)=4

-4sin(8x)=0

-sin(x)+2cos(x)=0

Frequently Asked Questions (FAQ)

What is the general solution for 8cos(6x)=2 ?
The general solution for 8cos(6x)=2 is x=(1.31811…)/6+(pin)/3 ,x= pi/3-(1.31811…)/6+(pin)/3