How do you differentiate the following parametric equation: # x(t)=cost, y(t)=sint #?

Answer 1

#(dy)/(dx)=-cott#

When we deal with parametric equations like #x=x(t)# and #y=y(t)#
#(dy)/(dx)=((dy)/(dt))/((dx)/(dt))#
Here we have #x(t)=cost# hence #((dx)/(dt))=-sint#
and #y(t)=sint# hence #((dy)/(dt))=cost#
Therefore #(dy)/(dx)=cost/(-sint)=-cott#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To differentiate the parametric equations x(t) = cos(t) and y(t) = sin(t) with respect to t, you simply differentiate each equation separately using the chain rule if necessary.

The derivative of x(t) = cos(t) with respect to t is dx/dt = -sin(t), and the derivative of y(t) = sin(t) with respect to t is dy/dt = cos(t).

So, the parametric differentiation results are: dx/dt = -sin(t), dy/dt = cos(t).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To differentiate the parametric equations (x(t) = \cos(t)) and (y(t) = \sin(t)) with respect to (t), you can use the chain rule. The chain rule states that if (y = f(u)) and (u = g(x)), then (\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}).

In this case, (x = \cos(t)) and (y = \sin(t)), so we have (x = f(t)) and (y = g(t)). Differentiating (x) and (y) with respect to (t) gives:

[\frac{dx}{dt} = -\sin(t)] [\frac{dy}{dt} = \cos(t)]

These are the derivatives of (x) and (y) with respect to (t), respectively.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7