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

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

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Popular >

solvefor x,z=arctan(x/y)

Solution

solve for

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

Solution

x = tan (z) y

Solution steps

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

Switch sides

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

Subtract

z

from both sides

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

Solve by substitution

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

Let:

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

u - z = 0

u - z = 0 : u = z

u - z = 0

Move

z

to the right side

u - z = 0

Add

z

to both sides

u - z + z = 0 + z

Simplify

u = z

u = z

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

Substitute back

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

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

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

Let:

u = \frac{x}{y}

arctan (u) - z = 0

Move

z

to the right side

arctan (u) - z = 0

Add

z

to both sides

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

Simplify

arctan (u) = z

arctan (u) = z

Apply trig inverse properties

arctan (u) = z

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

u = tan (z)

u = tan (z)

Substitute back

u = \frac{x}{y}

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

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

Multiply both sides by

y

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

Multiply both sides by

y

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

Simplify

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

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

x = tan (z) y

Popular Examples

-1/2 =cos(θ)

- \frac{1}{2} = cos (θ)

4cos^2(x)-3cos(x)-2=0

4 cos^{2} (x) - 3 cos (x) - 2 = 0

sin(x)=cos(3x)

sin (x) = cos (3 x)

solvefor x,y=5sin(x/4)solve for

x, y = 5 sin (\frac{x}{4})

3sin(pi/3 x)=2

3 sin (\frac{π}{3} x) = 2

Frequently Asked Questions (FAQ)

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