What is the general solution for 6cos(6x)=5 ?

The general solution for 6cos(6x)=5 is x=(0.58568…)/6+(pin)/3 ,x= pi/3-(0.58568…)/6+(pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6cos(6x)=5

Solution

6 cos (6 x) = 5

Solution

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

Degrees

x = 5.59288 \dots^{\circ} + 6 0^{\circ} n, x = 54.40711 \dots^{\circ} + 6 0^{\circ} n

Solution steps

6 cos (6 x) = 5

Divide both sides by

6

6 cos (6 x) = 5

Divide both sides by

6

\frac{6 cos ( 6 x )}{6} = \frac{5}{6}

Simplify

cos (6 x) = \frac{5}{6}

cos (6 x) = \frac{5}{6}

Apply trig inverse properties

cos (6 x) = \frac{5}{6}

General solutions for

cos (6 x) = \frac{5}{6}

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

6 x = arccos (\frac{5}{6}) + 2 πn, 6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

6 x = arccos (\frac{5}{6}) + 2 πn, 6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Solve

6 x = arccos (\frac{5}{6}) + 2 πn : x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{5}{6}) + 2 πn

Divide both sides by

6

6 x = arccos (\frac{5}{6}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

Simplify

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

Solve

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Divide both sides by

6

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

Simplify

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{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{5}{6} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{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{5}{6} )}{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{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

Popular Examples

4sec(x)+2sqrt(3)=sec(x)

4 sec (x) + 23 = sec (x)

sec(x)sin(x)=2

sec (x) sin (x) = 2

sec(x)cot(x)= 7/6

sec (x) cot (x) = \frac{7}{6}

tan(x)cos(x)=0

tan (x) cos (x) = 0

sin^2(x)-3sin(x)cos(x)+2cos^2(x)=0

sin^{2} (x) - 3 sin (x) cos (x) + 2 cos^{2} (x) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 6cos(6x)=5 ?
The general solution for 6cos(6x)=5 is x=(0.58568…)/6+(pin)/3 ,x= pi/3-(0.58568…)/6+(pin)/3