- #1
EconStudent
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Homework Statement
For the functions:
x = r*cos(θ)
y = r*sin(θ)
Calculate dθ/dX * dX/dθ (considering θ as a function of x, y) and simplify.
The Attempt at a Solution
I believe this should always be 1, by definition (as the product of a derivative and its inverse). However, I don't know how to show this.
Solving the first function for θ, I get cos-1(x/r). The derivative of this is a relatively messy expression 1 over the product of r and a square root, and its being multiplied by something relatively simple (-r*sin(θ)). Why is it that this would simplify to 1?
I get that the negatives and the r's will cancel. So it simplifies to:
sin(θ) / √(1 - x2/r2)
But I can't get any further nor am I satisfied that this expression is or is not equal to 1. Thanks in advance.