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Popular Trigonometry >

solvefor x,(sin(pix)+cos(piy))^5=36

Solution

solvefor

Solution

Solution steps

(sin (π x) + cos (π y))^{5} = 36

For

(g (x))^{n} = f (a)

, n is odd, the solution is

Solve

Move

cos (π y)

to the right side

Subtract

cos (π y)

from both sides

Simplify

The solution is

Apply trig inverse properties

General solutions for

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

Solve

Divide both sides by

π

Divide both sides by

π

Simplify

Solve

Divide both sides by

π

Divide both sides by

π

Simplify

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

Cancel

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

Graph

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