Find distances from angles
I have come across a problem I cannot seem to solve by myself, so I was hoping anyone on here could help me with this.
I'm sure it's pretty easy to do what I want, I just can't think of any way...
I'm studying physics at a university (first year) so you may assume that my math level is beyond highschool, but I'll tell you if I don't understand :P
Please consider the attached image.
The point P can move along the circle with radius R as shown.
Points 1 and 2 are fixed, seperated by a distance d. They are also centered around the origin so the x-coordinate of point 1 will be -1/2d and the x-coordinate of point 2 will be +1/2d. You get the point.
I'll try to explain in detail what I need, but if you don't need that, I'll ask the question first:
How can I express the lengths r1 and r2 in the angle a0?
I need to find the distances r1 and r2, based on the angle between the line OP and the x-axis (a0).
I need this for a physics project, where points 1 and 2 are two sound sources. I need to find the phase difference between source 1 and 2 at point P. Both sound sources are in phase, but because r2 < r1, there will be a phase difference at point P.
To find the phase difference, I need to know the lengths of r1 and r2.
I know, I could simply apply pythagoras or something, but I need to express these lengths in the angle that r0 makes with the x-axis (a0).
The reason behind this is that the two sound sources form a kind of directional speaker. They are placed at exactly the right distance apart (1/2 * wavelength) so their waves cancel out at the sides and add up right infront. Now I want to create a graph of the soundpressure (which depends on the phase difference) of both speakers combined at point P, which will vary with the angle a0.
So I need to express both lengths r1 and r2 in the angle a0 alone.
Does anyone know any way how to do this?