1. Warmup 12/1/15 How well do you relate to other people? What do you think is the key to a successful friendship? To summarize differentials up to this point pp 256: 5, 7, 9, 15 Objective Tonight’s Homework

2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

3. Notes on Proving Trigonometric Derivatives We’ve talked about trig derivatives before: d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) d/dx tan(x) = sec 2 (x)

4. Notes on Proving Trigonometric Derivatives We’ve talked about trig derivatives before: d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) d/dx tan(x) = sec 2 (x) But how do we prove these?

5. Notes on Proving Trigonometric Derivatives We’ve talked about trig derivatives before: d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) d/dx tan(x) = sec 2 (x) But how do we prove these? Let’s start by proving d/dx cos(x) = -sin(x) We’re going to do this by assuming that d/dx sin(x) = cos(x) We also will use the idea that cos(x)=sin( π /2-x)

6. Notes on Proving Trigonometric Derivatives Knowing all this, try to prove that: d/dx cos(x) = -sin(x)

7. Notes on Proving Trigonometric Derivatives Knowing all this, try to prove that: d/dx cos(x) = -sin(x) y = cos (x)start function y = sin( π /2-x)Other angle substitution u = π /2-xU definition du = -1 dximplicit differentiation y = sin(u)U substitution dy = cos(u) duimplicit differentiation dy = cos( π /2-x)(-1) dxsubstitution back dy = sin(x)(-1) dxOther angle substitution dy/dx = -sin(x)Rearranging π /2-x

8. Notes on Proving Trigonometric Derivatives We’ve now seen quite a number of rules. The rest of this section goes over much the same. There is a table on page 255 of your book. Copy this table down in your notes

9. Group Practice Look at the example problems on pages 253 through 255. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 256: 5, 7, 9, 15

10. Exit Question Does a function like Arcsin(x) have an integral? a) Yes b) Yes, but not at all values c) No d) Not enough information e) None of the above