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Popular >

cos(2x)=((6k-9))/9

Solution

cos (2 x) = \frac{( 6 k - 9 )}{9}

Solution

x = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn, x = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

Solution steps

cos (2 x) = \frac{( 6 k - 9 )}{9}

Simplify

\frac{6 k - 9}{9} : \frac{2 k - 3}{3}

\frac{6 k - 9}{9}

Factor

6 k - 9 : 3 (2 k - 3)

6 k - 9

Rewrite as

= 3 \cdot 2 k - 3 \cdot 3

Factor out common term

3

= 3 (2 k - 3)

= \frac{3 ( 2 k - 3 )}{9}

Cancel the common factor:

3

= \frac{2 k - 3}{3}

Apply trig inverse properties

cos (2 x) = \frac{2 k - 3}{3}

General solutions for

cos (2 x) = \frac{2 k - 3}{3}

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

2 x = arccos (\frac{2 k - 3}{3}) + 2 πn, 2 x = - arccos (\frac{2 k - 3}{3}) + 2 πn

2 x = arccos (\frac{2 k - 3}{3}) + 2 πn, 2 x = - arccos (\frac{2 k - 3}{3}) + 2 πn

Solve

2 x = arccos (\frac{2 k - 3}{3}) + 2 πn : x = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

2 x = arccos (\frac{2 k - 3}{3}) + 2 πn

Divide both sides by

2

2 x = arccos (\frac{2 k - 3}{3}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

x = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

Solve

2 x = - arccos (\frac{2 k - 3}{3}) + 2 πn : x = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

2 x = - arccos (\frac{2 k - 3}{3}) + 2 πn

Divide both sides by

2

2 x = - arccos (\frac{2 k - 3}{3}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

x = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

x = \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn, x = - \frac{arccos ( \frac{2 k - 3}{3} )}{2} + πn

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