calculate angle and distance from (x,y) coordinates

Question

How do I calculate the angle and distance of a point (x,y) from (0,0) for both possitive and negative values of x and y ?

Answer 1

The distance between 2 points is simply the Pythagorean theorem:

d = sqrt ( x^2 + y^2 )

Angle with what? Look at cos Θ = x / d

Answer 2

If the reference (where you start reading the angle) starts at the positive x axis then use the following:

x = r*cos(angle)

y = r*sin(angle)

r = d = square root of ( x² + y² ) = ( x² + y² )^1/2

where r is the radius or d distance formula.

of course the r = d equation above is because one of the points have a coordinate of (0,0). If none of the 2 points had coordinates of specifically exactly (0,0) the equation bellow would be used to find distance.

d = square root of ( (x₂-x₁)² + (y₂-y₁)² ) = ( (x₂-x₁)² + (y₂-y₁)² )^1/2

^{because r or d are magnitudes they will always be positive. Of course x and y can be negative but thanks to the angle you use. Remember:}

^{First Quadrant - from 0 to 90 degrees}

^{Second Quadrant - from 90 to 180 degrees}

Third quadrant - from 180 to 270 degrees

Fourth Quadrant - from 270 to 360 degrees

Check unit circle on google, it also has info on radians. Remember when using a calculator if you plug values in degrees your calculator must be on degrees. If you plug radians values of course calculator must be on radians.

feel free to ask if more questions.

Hope this helps. Have a good day!