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Popular Trigonometry >

18cos(10x)+2=10

Solution

18 cos (10 x) + 2 = 10

Solution

x = \frac{1.11024 \dots}{10} + \frac{πn}{5}, x = \frac{π}{5} - \frac{1.11024 \dots}{10} + \frac{πn}{5}

+1

Degrees

x = 6.36122 \dots^{\circ} + 3 6^{\circ} n, x = 29.63877 \dots^{\circ} + 3 6^{\circ} n

Solution steps

18 cos (10 x) + 2 = 10

Move

2

to the right side

18 cos (10 x) + 2 = 10

Subtract

2

from both sides

18 cos (10 x) + 2 - 2 = 10 - 2

Simplify

18 cos (10 x) = 8

18 cos (10 x) = 8

Divide both sides by

18

18 cos (10 x) = 8

Divide both sides by

18

\frac{18 cos ( 10 x )}{18} = \frac{8}{18}

Simplify

cos (10 x) = \frac{4}{9}

cos (10 x) = \frac{4}{9}

Apply trig inverse properties

cos (10 x) = \frac{4}{9}

General solutions for

cos (10 x) = \frac{4}{9}

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

10 x = arccos (\frac{4}{9}) + 2 πn, 10 x = 2 π - arccos (\frac{4}{9}) + 2 πn

10 x = arccos (\frac{4}{9}) + 2 πn, 10 x = 2 π - arccos (\frac{4}{9}) + 2 πn

Solve

10 x = arccos (\frac{4}{9}) + 2 πn : x = \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

10 x = arccos (\frac{4}{9}) + 2 πn

Divide both sides by

10

10 x = arccos (\frac{4}{9}) + 2 πn

Divide both sides by

10

\frac{10 x}{10} = \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10}

Simplify

x = \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

x = \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

Solve

10 x = 2 π - arccos (\frac{4}{9}) + 2 πn : x = \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

10 x = 2 π - arccos (\frac{4}{9}) + 2 πn

Divide both sides by

10

10 x = 2 π - arccos (\frac{4}{9}) + 2 πn

Divide both sides by

10

\frac{10 x}{10} = \frac{2 π}{10} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} = \frac{2 π}{10} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} : x

\frac{10 x}{10}

Divide the numbers:

\frac{10}{10} = 1

= x

Simplify

\frac{2 π}{10} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10} : \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

\frac{2 π}{10} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10}

Cancel

\frac{2 π}{10} : \frac{π}{5}

\frac{2 π}{10}

Cancel the common factor:

2

= \frac{π}{5}

= \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{2 πn}{10}

Cancel

\frac{2 πn}{10} : \frac{πn}{5}

\frac{2 πn}{10}

Cancel the common factor:

2

= \frac{πn}{5}

= \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

x = \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

x = \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

x = \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

x = \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}, x = \frac{π}{5} - \frac{arccos ( \frac{4}{9} )}{10} + \frac{πn}{5}

Show solutions in decimal form

x = \frac{1.11024 \dots}{10} + \frac{πn}{5}, x = \frac{π}{5} - \frac{1.11024 \dots}{10} + \frac{πn}{5}

Graph

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