What is the general solution for 7cos(6x)=2 ?

The general solution for 7cos(6x)=2 is x=(1.28104…)/6+(pin)/3 ,x= pi/3-(1.28104…)/6+(pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7cos(6x)=2

Solution

7 cos (6 x) = 2

Solution

x = \frac{1.28104 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.28104 \dots}{6} + \frac{πn}{3}

Degrees

x = 12.23307 \dots^{\circ} + 6 0^{\circ} n, x = 47.76692 \dots^{\circ} + 6 0^{\circ} n

Solution steps

7 cos (6 x) = 2

Divide both sides by

7

7 cos (6 x) = 2

Divide both sides by

7

\frac{7 cos ( 6 x )}{7} = \frac{2}{7}

Simplify

cos (6 x) = \frac{2}{7}

cos (6 x) = \frac{2}{7}

Apply trig inverse properties

cos (6 x) = \frac{2}{7}

General solutions for

cos (6 x) = \frac{2}{7}

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

6 x = arccos (\frac{2}{7}) + 2 πn, 6 x = 2 π - arccos (\frac{2}{7}) + 2 πn

6 x = arccos (\frac{2}{7}) + 2 πn, 6 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Solve

6 x = arccos (\frac{2}{7}) + 2 πn : x = \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

6

6 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{arccos ( \frac{2}{7} )}{6} + \frac{2 πn}{6}

Simplify

x = \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

Solve

6 x = 2 π - arccos (\frac{2}{7}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

6

6 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{2 πn}{6}

Simplify

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{2}{7} )}{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{2}{7} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{2}{7} )}{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{2}{7} )}{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{2}{7} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{2}{7} )}{6} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{1.28104 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{1.28104 \dots}{6} + \frac{πn}{3}

Popular Examples

sin^2(θ)+cos(θ)(1-cos(θ))=0

sin^{2} (θ) + cos (θ) (1 - cos (θ)) = 0

tan(A)= 94/67

tan (A) = \frac{94}{67}

2tan(2x)-10=34641

2 tan (2 x) - 10 = 34641

cos(θ)=0.5747

cos (θ) = 0.5747

0=(110cos(377t))/8

0 = \frac{110 cos ( 377 t )}{8}

Frequently Asked Questions (FAQ)

What is the general solution for 7cos(6x)=2 ?
The general solution for 7cos(6x)=2 is x=(1.28104…)/6+(pin)/3 ,x= pi/3-(1.28104…)/6+(pin)/3