x, y, and theta in a plane (changing coordinates)

[OhMrsDarcy]

The problem reads:

Suppose we have a point (x, y) on a plane. If we let r be the distance to (x, y) and theta be the angle that has (x, y) on its terminal side, then (r, theta) is the ordered pair that describes the same point.

a) How do you compute the x,y-coordinates of a point given by (r,theta)?

b) How do you compute the r,theta-coordinates of a point given by (x,y)?

Thanks,
Bri

 

[galactus]

If you're given a radius and angle \(\displaystyle (r, {\theta})\) you can use sine and cosine.

\(\displaystyle rsin({\theta})=y\)

\(\displaystyle rcos({\theta})=x\)


The other way around. If you're given (x,y):

Find the radius by using Pythagoras: \(\displaystyle r=\sqrt{x^{2}+y^{2}}\)

Then \(\displaystyle cos({\theta})=\frac{x}{r}\)

\(\displaystyle sin({\theta})=\frac{y}{r}\)

 

[OhMrsDarcy]

Thanks so much! We're just beginning this whole section, so everything is all new and confusing. But that makes total sense!

~Bri