Transcript 5 1 Fundamental Identities 02

Objective:
1. To rewrite and
simplify trig
expressions using
trig identities
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Assignment:
P. 379: 27-44 S
P. 380: 45-56
P. 380: 57-60 S
P. 381: 113, 114
Homework
Supplement
You will be able to rewrite and
simplify trig expressions using
trig identities
When simplifying and rewriting trig expressions,
here are some things to try:
1. Substitute part of the expression with an
identity
2. Factor or FOIL
3. Write as a single trig function
4. Rewrite as sine and cosine only
5. Combine fractions
You may remember
these identities
fondly from
previous lessons.
Now we’ll be using
them to simplify
and rewrite trig
expressions.
Practice doing this
will make solving
trig equations
easier.
Factoring trig expressions is just like factoring
algebraic fractions.
k  1   k  1 k  1
2
cos 2 x  1   cos x  1 cos x  1
Factoring trig expressions is just like factoring
algebraic fractions.
3k  4k  15   3k  5 k  3
2
3cos 2 x  4 cos x  15   3cos x  5 cos x  3
Factor and simplify:
1  sin 2 
1  sin 
Factor and simplify:
csc   1
csc 2   1
Factor and simplify:
2 csc x  7 csc x  6
2
Factor and simplify:
4 tan 2 x  tan x  3
Factor and simplify:
sec x  3 tan x  1
2
Factor and simplify:
csc x  cot x  3
2
Factor and simplify:
tan x  tan x  3 tan x  3
3
2
Factor and simplify:
8cos x  4 cos x  50 cos x  25
3
2
Factor and simplify:
8sin x  4sin x  10sin x  3sin x  3
4
3
2
Factor and simplify:
6sec x  sec x  25 tan x  4sec x  21
4
3
2
Factor and simplify:
csc x  27
3
Factor and simplify:
6 cot x  6 csc x
3
3
Factor and simplify:
sin x  cos x
12
12
Objective:
1. To rewrite and
simplify trig
expressions using
trig identities
•
•
•
•
•
Assignment:
P. 379: 27-44 S
P. 380: 45-56
P. 380: 57-60 S
P. 381: 113, 114
Homework
Supplement