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

The general solution for solvefor x,u=arctan(x/y) is x=tan(u)y

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Popular >

solvefor x,u=arctan(x/y)

Solution

solve for

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

Solution

x = tan (u) y

Solution steps

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

Switch sides

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

Subtract

u

from both sides

arctan (\frac{x}{y}) - u = 0

Solve by substitution

arctan (\frac{x}{y}) - u = 0

Let:

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

v - u = 0

v - u = 0 : v = u

v - u = 0

Move

u

to the right side

v - u = 0

Add

u

to both sides

v - u + u = 0 + u

Simplify

v = u

v = u

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

Substitute back

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

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

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

Let:

v = \frac{x}{y}

arctan (v) - u = 0

Move

u

to the right side

arctan (v) - u = 0

Add

u

to both sides

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

Simplify

arctan (v) = u

arctan (v) = u

Apply trig inverse properties

arctan (v) = u

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

v = tan (u)

v = tan (u)

Substitute back

v = \frac{x}{y}

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

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

Multiply both sides by

y

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

Multiply both sides by

y

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

Simplify

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

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

x = tan (u) y

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Frequently Asked Questions (FAQ)

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