Problem with inversion of the system u=\frac{\cos\theta}{1-t\cos\theta} , \ v=\frac{\sin\theta}{1+t\sin\theta}

Maximillian Patterson

Maximillian Patterson

Answered question

2022-04-28

Problem with inversion of the system u=cosθ1tcosθ, v=sinθ1+tsinθ

Answer & Explanation

eslasadanv3

eslasadanv3

Beginner2022-04-29Added 20 answers

One way is to invert each equality and then you can solve them for sinθ and cosθ. Then, use sin2θ+cos2θ=1 to get rid of θ and solve for t. Having t as a function of u and v, you can find sinθ+cosθ easily.
haillarip0c9

haillarip0c9

Beginner2022-04-30Added 23 answers

You have:
cosθ=u1+ut  and  sinθ=v1vt
Now use sin2θ+cos2θ=1
u2(1+ut)2+v2(1vt)2=1
olving the above equation you will get equation in t and then you can find t as a function of u and v

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?