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Popular >

solvefor x,y-cos(x)=sin(y)

Solution

solve for

x, y - cos (x) = sin (y)

Solution

x = arccos (- sin (y) + y) + 2 πn, x = - arccos (- sin (y) + y) + 2 πn

Solution steps

y - cos (x) = sin (y)

Move

y

to the right side

y - cos (x) = sin (y)

Subtract

y

from both sides

y - cos (x) - y = sin (y) - y

Simplify

- cos (x) = sin (y) - y

- cos (x) = sin (y) - y

Divide both sides by

- 1

- cos (x) = sin (y) - y

Divide both sides by

- 1

\frac{- cos ( x )}{- 1} = \frac{sin ( y )}{- 1} - \frac{y}{- 1}

Simplify

\frac{- cos ( x )}{- 1} = \frac{sin ( y )}{- 1} - \frac{y}{- 1}

Simplify

\frac{- cos ( x )}{- 1} : cos (x)

\frac{- cos ( x )}{- 1}

Apply the fraction rule:

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

= \frac{cos ( x )}{1}

Apply rule

\frac{a}{1} = a

= cos (x)

Simplify

\frac{sin ( y )}{- 1} - \frac{y}{- 1} : - sin (y) + y

\frac{sin ( y )}{- 1} - \frac{y}{- 1}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sin ( y ) - y}{- 1}

Apply the fraction rule:

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

= - \frac{sin ( y ) - y}{1}

Apply rule

\frac{a}{1} = a

= - (sin (y) - y)

Distribute parentheses

= - sin (y) - (- y)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - sin (y) + y

cos (x) = - sin (y) + y

cos (x) = - sin (y) + y

cos (x) = - sin (y) + y

Apply trig inverse properties

cos (x) = - sin (y) + y

General solutions for

cos (x) = - sin (y) + y

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

x = arccos (- sin (y) + y) + 2 πn, x = - arccos (- sin (y) + y) + 2 πn

x = arccos (- sin (y) + y) + 2 πn, x = - arccos (- sin (y) + y) + 2 πn

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2(1-cos^2(x))-cos(x)-1=0

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