 Let's take a look at an example of using derivatives to find the slope of a trigonometric curve at specified points. So here we have the curve f of x equals 2 cosine of x and we have three points on that curve given to us and we are trying to find the slope at each of those points. So of course the slope is going to be given to us by the derivative, which in this case the derivative would be negative 2 sine of x. Now this would very much be a non-calculator problem and is going to require use of your unit circle knowledge. So the first one we want the derivative at the x value negative pi over 2. So we need to think of the unit circle. Sine of a negative pi over 2 is going to be negative 1, so our slope is simply 2. Now these would be really easy for you to check on your graphing calculator if you want to do that. Practice your graphing calculator skills, good opportunity for that. So now we're going to find the derivative at the x value pi over 3. So we have negative 2, now we need to think of the sine of pi over 3, remember that's going to be square root of 3 over 2, so there we have negative root 3. So you can see what's happening. If you think about the meaning of your derivatives coming out positive or negative at the x value of negative pi over 2, our derivative value there was a positive 2, so remember that means that that particular point the curve is increasing, whereas at the x value of pi over 3 our derivative came out negative, so that means that that particular point on the curve, the curve is decreasing. Now let's see what happens at pi. So we have negative 2, now we need to think of the sine of pi which is 0, so that's coming out 0, so think about what that tells us. That tells us there's going to be a horizontal tangent there, and most likely, and you can look at the curve to confirm this, it is going to be either a maximum or a minimum, you can easily look at the curve to tell that. But simply because of the fact that the derivative came out as 0, we do know there is a horizontal tangent on the curve at that location.