Title: FP2 (MEI) Calculus (part 1) Using trigonometric identities in integration, the inverse trigonometric functions, differentiation of functions involving inverse trigonometric functions.
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2FP2 (MEI)Calculus (part 1) Using trigonometric
identities in integration, the inverse
trigonometric functions, differentiation of
functions involving inverse trigonometric
functions.
- Let Maths take you Further
3Using trigonometric identities in integration,
the inverse trigonometric functions,
differentiation of functions involving inverse
trigonometric functions.
- Before you start
- You need to be familiar with the laws of indices
(Core 1 chapter 5) and logarithms (Core 2 chapter
11). - You need to have covered all of the work on
functions in Core 3 chapter 3. In particular, the
section on inverse trigonometrical functions on
pages 45 - 46 is a useful introduction. - You need to be confident with all the techniques
of differentiation and integration in C2 and C3,
in particular differentiation using the chain
rule, differentiation of trigonometric functions,
implicit differentiation (C3 chapter 4),
integration by substitution and integration of
trigonometric functions (C3 chapter 5). - You must also be confident with all the work on
Trigonometry covered so far (C2 chapter 10 and C4
chapter 8). In particular, the enrichment work on
pages 218 222 of the A2 Pure Mathematics
textbook covers some of the work in this section.
4Using trigonometric identities in integration,
the inverse trigonometric functions,
differentiation of functions involving inverse
trigonometric functions.
- When you have finishedYou should
- Be able to use trigonometric identities to
integrate functions such as sin2 x, sin3 x, sin 4
x, tan x. - Understand the definitions of inverse
trigonometric functions. - Be able to differentiate inverse trigonometric
functions.
5Calculus - Reminder
6Calculus - Reminder
7Integration of powers of sine and cosine
We can use this result to integrate odd powers of
sine for example
8Try
9Even powers of sine and cosine
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11Inverse trigonometric functions
It is useful to look at the graph of a function
together with its inverse (use of autograph)
12arcsin
13arccos
14arctan
15Look at yarcsecx on autograph and consider its
domain and range (if time permits)
Example show that
16Differentiating inverse trigonometric functions
Use autograph to draw the gradient function of
yarcsinx
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19Summary of results (these are given in the exam
formula book)
Now that we have these results we can use the
chain rule to differentiate composite functions
that include inverse trigonometric functions
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23Using trigonometric identities in integration,
The inverse trigonometric functions,
Differentiation of functions involving inverse
trigonometric functions.
- When you have finishedYou should
- Be able to use trigonometric identities to
integrate functions such as sin2 x, sin3 x, sin 4
x, tan x. - Understand the definitions of inverse
trigonometric functions. - Be able to differentiate inverse trigonometric
functions.
24Independent study
- Using the MEI online resources complete the study
plan for Calculus 1 - Do the online multiple choice test for this and
submit your answers online.