# Thread: I calculated the curvature, but I want to make sure I did it correctly.

1. ## I calculated the curvature, but I want to make sure I did it correctly.

1. Consider the parametric curve f(t)= [ 4 (sin(3t))^2, 1-(cos(3t))^2, 2-2 (cos(3t))^2]. Calculate its curvature. What conclusion can you make about the curve based on this curvature?

2. ## Re: I calculated the curvature, but I want to make sure I did it correctly.

Hey kandygirl16.

What did you obtain for the result? Is it positive, negative or zero? What can you conclude given it's sign?

3. ## Re: I calculated the curvature, but I want to make sure I did it correctly.

Originally Posted by kandygirl16
1. Consider the parametric curve f(t)= [ 4 (sin(3t))^2, 1-(cos(3t))^2, 2-2 (cos(3t))^2]. Calculate its curvature. What conclusion can you make about the curve based on this curvature?
Do you know that curvature is $\kappa (t) = \frac{{\left\| {f'(t) \times f''(t)} \right\|}}{{\left\| {f'(t)} \right\|}}~?$

4. ## Re: I calculated the curvature, but I want to make sure I did it correctly.

something like that, we use a different formula though