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Popular >

solvefor x,ln(y)+y^2=-cos(x)

Solution

solve for

x, ln (y) + y^{2} = - cos (x)

Solution

x = arccos (- ln (y) - y^{2}) + 2 πn, x = - arccos (- ln (y) - y^{2}) + 2 πn

Solution steps

ln (y) + y^{2} = - cos (x)

Move

cos (x)

to the left side

ln (y) + y^{2} = - cos (x)

Add

cos (x)

to both sides

ln (y) + y^{2} + cos (x) = - cos (x) + cos (x)

Simplify

ln (y) + y^{2} + cos (x) = 0

ln (y) + y^{2} + cos (x) = 0

Move

ln (y)

to the right side

ln (y) + y^{2} + cos (x) = 0

Subtract

ln (y)

from both sides

ln (y) + y^{2} + cos (x) - ln (y) = 0 - ln (y)

Simplify

y^{2} + cos (x) = - ln (y)

y^{2} + cos (x) = - ln (y)

Move

y^{2}

to the right side

y^{2} + cos (x) = - ln (y)

Subtract

y^{2}

from both sides

y^{2} + cos (x) - y^{2} = - ln (y) - y^{2}

Simplify

cos (x) = - ln (y) - y^{2}

cos (x) = - ln (y) - y^{2}

Apply trig inverse properties

cos (x) = - ln (y) - y^{2}

General solutions for

cos (x) = - ln (y) - y^{2}

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

x = arccos (- ln (y) - y^{2}) + 2 πn, x = - arccos (- ln (y) - y^{2}) + 2 πn

x = arccos (- ln (y) - y^{2}) + 2 πn, x = - arccos (- ln (y) - y^{2}) + 2 πn

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