What is the general solution for cos(xpi)=(-1)^n ?

The general solution for cos(xpi)=(-1)^n is x=(arccos((-1)^n))/pi+2k,x=-(arccos((-1)^n))/pi+2k

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cos(xpi)=(-1)^n

cos (x π) = (- 1)^{n}

x = \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k, x = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

Solution steps

cos (x π) = (- 1)^{n}

Apply trig inverse properties

cos (x π) = (- 1)^{n}

General solutions for

cos (x π) = (- 1)^{n}

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

x π = arccos ((- 1)^{n}) + 2 πk, x π = - arccos ((- 1)^{n}) + 2 πk

x π = arccos ((- 1)^{n}) + 2 πk, x π = - arccos ((- 1)^{n}) + 2 πk

Solve

x π = arccos ((- 1)^{n}) + 2 πk : x = \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

x π = arccos ((- 1)^{n}) + 2 πk

Divide both sides by

π

x π = arccos ((- 1)^{n}) + 2 πk

Divide both sides by

π

\frac{x π}{π} = \frac{arccos ( ( - 1 ) ^{n} )}{π} + \frac{2 πk}{π}

Simplify

x = \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

x = \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

Solve

x π = - arccos ((- 1)^{n}) + 2 πk : x = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

x π = - arccos ((- 1)^{n}) + 2 πk

Divide both sides by

π

x π = - arccos ((- 1)^{n}) + 2 πk

Divide both sides by

π

\frac{x π}{π} = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + \frac{2 πk}{π}

Simplify

x = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

x = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

x = \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k, x = - \frac{arccos ( ( - 1 ) ^{n} )}{π} + 2 k

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cos^{3} (x) = \frac{1}{4 ( 3 cos ( x ) + cos ( 3 x ) )}

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6 sin (\frac{π}{4} x) = 3

What is the general solution for cos(xpi)=(-1)^n ?
The general solution for cos(xpi)=(-1)^n is x=(arccos((-1)^n))/pi+2k,x=-(arccos((-1)^n))/pi+2k