Bayes Theorem

Step 1: Use the identity involving inverse trigonometric functions.
We are given the equation:

%5Ccos%5E%7B-1%7D(x-2)%20%3D%20%5Csin%5E%7B-1%7D(y%2B1)

We know that

%5Ccos%5E%7B-1%7D%20%5Ctheta%20%2B%20%5Csin%5E%7B-1%7D%20%5Ctheta%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D

for all

%5Ctheta

in the domain

%5B0%2C%201%5D

. Using this identity, we can rewrite the equation as:

%5Ccos%5E%7B-1%7D(x-2)%20%2B%20%5Ccos%5E%7B-1%7D(y%2B1)%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D

Step 2: Solve for

x

and

y

.
Now, apply the identity

%5Ccos%5E%7B-1%7D%20%5Ctheta%20%3D%20%5Csin%5E%7B-1%7D%20%5Csqrt%7B1%20-%20%5Ctheta%5E2%7D

to express both terms in a solvable form, and we eventually get the equation of the curve:

(x%20-%202)%5E2%20%2B%20(y%20%2B%201)%5E2%20%3D%201

This represents a circle.

Chapter Questions
2 MCQs