Warmup 12/1/15
How well do you relate to other people? What do you
think is the key to a successful friendship?
Objective
Tonight’s Homework
To summarize differentials up
to this point
pp 256: 5, 7, 9, 15
Homework Help
Let’s spend the first 10 minutes of class going over any
problems with which you need help.
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) = sec2(x)
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) = sec2(x)
But how do we prove these?
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) = sec2(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)
Notes on Proving Trigonometric Derivatives
Knowing all this, try to prove that:
d/dx cos(x) = -sin(x)
Notes on Proving Trigonometric Derivatives
Knowing all this, try to prove that:
d/dx cos(x) = -sin(x)
y = cos (x)
y = sin(π/2-x)
start function
Other angle substitution
u = π/2-x
du = -1 dx
U definition
implicit differentiation
y = sin(u)
U substitution
dy = cos(u) du
implicit differentiation
dy = cos(π/2-x)(-1) dx substitution back
dy = sin(x)(-1) dx
Other angle substitution
dy/dx = -sin(x)
Rearranging π/2-x
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
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
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