how do you convert parametric form to polar form?

Question

im not sure how and i have a test tomorrow.
sample prbo: x=3cos(30)T
y=3sin(30)T
do you just do 3sin(30)T/3cos(30)T to find theta and (3sin(30)T)^2+(3cos(30)T)^2 to find r^2?
if not, please explain.

Answer 1

Well, remember that the usual equations for x and y in polar coordinates are:

x = r cos θ

and

y = r sin θ

So in this case, θ should be obvious...it's just 30°.

But you could still find it the way you mentioned:

tan θ = y/x = (3t sin 30°)/(3t cos 30°) = sin 30°/cos 30° = tan 30°

So θ = 30°.

And yes, your formula for r² is correct too.

When you simplify it, you should find that:

r = 3t√2

If my guess is correct.

Answer 2

r = -2/sin? y = r sin? = -2 sin?/sin? y = -2 ================== r = (a million/cos?) + 3 x = r cos? = a million + 3 cos? y = r sin ? = tan? + 3sin? = (y/x) + 3 sin? 3 cos? = x - a million 3 sin ? = y - (y/x) 9 cos²? + 9 sin²? = (x - a million)² + [y - (y/x)]² (x - a million)² + [y - (y/x)]² = 9