What is the general solution for solvefor y,x+arctan(y/x)=0 ?

The general solution for solvefor y,x+arctan(y/x)=0 is y=tan(-x)x

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Popular >

solvefor y,x+arctan(y/x)=0

Solution

solve for

y, x + arctan (\frac{y}{x}) = 0

Solution

y = tan (- x) x

Solution steps

x + arctan (\frac{y}{x}) = 0

Solve by substitution

x + arctan (\frac{y}{x}) = 0

Let:

arctan (\frac{y}{x}) = u

x + u = 0

x + u = 0 : u = - x

x + u = 0

Move

x

to the right side

x + u = 0

Subtract

x

from both sides

x + u - x = 0 - x

Simplify

u = - x

u = - x

arctan (\frac{y}{x}) = - x

Substitute back

u = arctan (\frac{y}{x})

arctan (\frac{y}{x}) = - x

arctan (\frac{y}{x}) = - x

Solve by substitution

x + arctan (\frac{y}{x}) = 0

Let:

arctan (\frac{y}{x}) = u

x + u = 0

x + u = 0 : u = - x

x + u = 0

Move

x

to the right side

x + u = 0

Subtract

x

from both sides

x + u - x = 0 - x

Simplify

u = - x

u = - x

arctan (\frac{y}{x}) = - x

Substitute back

u = arctan (\frac{y}{x})

arctan (\frac{y}{x}) = - x

arctan (\frac{y}{x}) = - x

Let:

u = \frac{y}{x}

x + arctan (u) = 0

Move

x

to the right side

x + arctan (u) = 0

Subtract

x

from both sides

x + arctan (u) - x = 0 - x

Simplify

arctan (u) = - x

arctan (u) = - x

Apply trig inverse properties

arctan (u) = - x

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

u = tan (- x)

u = tan (- x)

Substitute back

u = \frac{y}{x}

\frac{y}{x} = tan (- x) : y = tan (- x) x; x \neq = 0

\frac{y}{x} = tan (- x)

Multiply both sides by

x

\frac{y}{x} = tan (- x)

Multiply both sides by

x

\frac{y x}{x} = tan (- x) x; x \neq = 0

Simplify

y = tan (- x) x; x \neq = 0

y = tan (- x) x; x \neq = 0

y = tan (- x) x

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor y,x+arctan(y/x)=0 ?
The general solution for solvefor y,x+arctan(y/x)=0 is y=tan(-x)x