What is the general solution for c^9=3tan(-3x+c) ?

The general solution for c^9=3tan(-3x+c) is x=-(arctan((c^9)/3))/(3)-(pin)/3+c/3

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c^9=3tan(-3x+c)

Solution

c^{9} = 3 tan (- 3 x + c)

Solution

x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

Solution steps

c^{9} = 3 tan (- 3 x + c)

Switch sides

3 tan (- 3 x + c) = c^{9}

Divide both sides by

3

3 tan (- 3 x + c) = c^{9}

Divide both sides by

3

\frac{3 tan ( - 3 x + c )}{3} = \frac{c ^{9}}{3}

Simplify

tan (- 3 x + c) = \frac{c ^{9}}{3}

tan (- 3 x + c) = \frac{c ^{9}}{3}

Apply trig inverse properties

tan (- 3 x + c) = \frac{c ^{9}}{3}

General solutions for

tan (- 3 x + c) = \frac{c ^{9}}{3}

tan (x) = a \Rightarrow x = arctan (a) + πn

- 3 x + c = arctan (\frac{c ^{9}}{3}) + πn

- 3 x + c = arctan (\frac{c ^{9}}{3}) + πn

Solve

- 3 x + c = arctan (\frac{c ^{9}}{3}) + πn : x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

- 3 x + c = arctan (\frac{c ^{9}}{3}) + πn

Move

c

to the right side

- 3 x + c = arctan (\frac{c ^{9}}{3}) + πn

Subtract

c

from both sides

- 3 x + c - c = arctan (\frac{c ^{9}}{3}) + πn - c

Simplify

- 3 x = arctan (\frac{c ^{9}}{3}) + πn - c

- 3 x = arctan (\frac{c ^{9}}{3}) + πn - c

Divide both sides by

- 3

- 3 x = arctan (\frac{c ^{9}}{3}) + πn - c

Divide both sides by

- 3

\frac{- 3 x}{- 3} = \frac{arctan ( \frac{c ^{9}}{3} )}{- 3} + \frac{πn}{- 3} - \frac{c}{- 3}

Simplify

\frac{- 3 x}{- 3} = \frac{arctan ( \frac{c ^{9}}{3} )}{- 3} + \frac{πn}{- 3} - \frac{c}{- 3}

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{arctan ( \frac{c ^{9}}{3} )}{- 3} + \frac{πn}{- 3} - \frac{c}{- 3} : - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

\frac{arctan ( \frac{c ^{9}}{3} )}{- 3} + \frac{πn}{- 3} - \frac{c}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arctan ( \frac{c ^{9}}{3} )}{3} + \frac{πn}{- 3} - \frac{c}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} - \frac{c}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} - (- \frac{c}{3})

Apply rule

- (- a) = a

= - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

x = - \frac{arctan ( \frac{c ^{9}}{3} )}{3} - \frac{πn}{3} + \frac{c}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for c^9=3tan(-3x+c) ?
The general solution for c^9=3tan(-3x+c) is x=-(arctan((c^9)/3))/(3)-(pin)/3+c/3