# Thread: Graphing Trigonometric Functions and computing their derivative

1. ## Graphing Trigonometric Functions and computing their derivative

For an upcoming midterm, I need to be able to do the following: graph, indicate direction & speed, compute the derivative, and find critical points of trigonometric and hyperbolic functions.

For example:

$\displaystyle (sin\theta, cos\theta)$

$\displaystyle (csc\theta, cot\theta) \theta \neq k\pi, k\in Z$

$\displaystyle (cosh t, sinh t)$

What perplexes me is the form: (a, x) with respect to theta. Are these parametric plots or the two functions mapped onto one plot? My interpretation is that they are parametric. So, for example,

$\displaystyle (sin\theta, cos\theta)$

Should be a unit circle except $\displaystyle sin\theta = x$ and $\displaystyle cos\theta = y$

If this is true, do I take the derivative of $\displaystyle sin\theta = x => cos\theta$ and $\displaystyle cos\theta = y => -sin\theta$?

But then the plot of its derivative is also graphically the same as the original function. Any help would be greatly appreciated, thanks for your time.

2. If you are correct that

$\displaystyle (\cos(\theta),\sin(\theta))$ is parametric then to find the derivative you can use this formula

if
$\displaystyle x=\cos(\theta);y=\sin(\theta)$
Then
$\displaystyle \displaystyle \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{ d\theta}}=\frac{\cos(\theta)}{-\sin(\theta)}$