Lesson Plan #6
Lesson Plan #88
Class: PreCalculus Date: Tuesday May 27th, 2014
Topic: Derivatives of Sine and Cosine functions Aim: How do we differentiate trigonometric functions?
Objectives:
1) Students will be able to differentiate trigonometric functions
HW# 88:
Do Now:
1) Evaluate [pic] 2) [pic]
Procedure:
Write the Aim and Do Now
Get students working!
Take attendance
Give back work
Go over the HW
Collect HW
Go over the Do Now
Recall the long way to find the derivative. Let’s use this long way to find the derivative of [pic]
[pic]
Use the formula for the sin of the sum of angles to expand the first part of the limit
[pic]
Rewrite the right side of the equation so that the middle term is first, the last term is in the middle and the middle term is last
[pic]
Factor [pic]from the last two terms
[pic]
Put the denominator under each term of the numerator
[pic]
Evaluate limit
[pic]
[pic]
So we have the derivative of[pic].
[pic]
By other proofs we can get the derivatives of the other five trigonometric functions. Below are the derivatives of the six trig functions.
Assignment:
I. Find the derivative of each of the following
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic]
6) [pic]
7) [pic]
III. Find the slope of the line tangent to [pic]at [pic]radian
Sample Test Questions:
1) If [pic], find [pic]
2) Find [pic]if [pic]
A) [pic] B) [pic] C) [pic]
D) [pic] E) [pic]
3) The equation of the tangent to the curve [pic]at the point [pic]is
A) [pic] B) [pic] C) [pic] D) [pic] E) [pic]
4)
5.
6.
7.
8.
9.
10.
11.
12.
13.
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Definition of the Derivative of a Function: The derivative of a [pic]at [pic] is given by
[pic] provided the limit exists
[pic] [pic]
[pic] [pic]
[pic] [pic]
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