What is the general solution for 5cos(6x)+6=9 ?

The general solution for 5cos(6x)+6=9 is x=(0.92729…)/6+(pin)/3 ,x= pi/3-(0.92729…)/6+(pin)/3

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Popular >

5cos(6x)+6=9

Solution

5 cos (6 x) + 6 = 9

Solution

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

Degrees

x = 8.85501 \dots^{\circ} + 6 0^{\circ} n, x = 51.14498 \dots^{\circ} + 6 0^{\circ} n

Solution steps

5 cos (6 x) + 6 = 9

Move

6

to the right side

5 cos (6 x) + 6 = 9

Subtract

6

from both sides

5 cos (6 x) + 6 - 6 = 9 - 6

Simplify

5 cos (6 x) = 3

5 cos (6 x) = 3

Divide both sides by

5

5 cos (6 x) = 3

Divide both sides by

5

\frac{5 cos ( 6 x )}{5} = \frac{3}{5}

Simplify

cos (6 x) = \frac{3}{5}

cos (6 x) = \frac{3}{5}

Apply trig inverse properties

cos (6 x) = \frac{3}{5}

General solutions for

cos (6 x) = \frac{3}{5}

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

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

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

Solve

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

6 x = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

6

6 x = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

6

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

Simplify

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

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

Solve

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

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

Divide both sides by

6

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

Divide both sides by

6

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

Simplify

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

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

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

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

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

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

Show solutions in decimal form

x = \frac{0.92729 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{6} + \frac{πn}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for 5cos(6x)+6=9 ?
The general solution for 5cos(6x)+6=9 is x=(0.92729…)/6+(pin)/3 ,x= pi/3-(0.92729…)/6+(pin)/3