1. Using Fundamental Identities
5.1
Using Fundamental Identities
Ex. 1. Given sec u = -
and tan u > 0
Find all 6 trig. Functions.
Solution: Where is sec u negative and tan u positive?
Sec is (-) in quadrants 2 & 3
Tan is (+) in quadrants 1 & 3
III -2 3

2. Ex.’s
Simplify: sin x cos2 x - sin x =
sin x
(cos2 x - 1)
= sin x
(-sin2 x)
= -sin3 x
Factor: sec2 x - 1
= (sec x - 1)(sec x + 1)
4 tan2 x + tan x - 3 =
(4tan x - 3)(tan x + 1)
Factor: csc2 x - cot x - 3
(1 + cot2 x) - cot x - 3
= (cot2 x - cot x - 2)
(cot x - 2)(cot x + 1)

3. Simplify: sin t + cot t cos t
Now, get common
denominators

4. Rewriting a Trigonometric Expression
HW pg 379
1-43 odd
= sec2 x - tan x sec x

5. Ex. Combining Fractional Expressions
(sin x)(sin x) + (cos x)(1 + cos x)
(1 + cos x) (sin x)

6. Trigonometric Substitution
Use x = 2tan , to express as a function of
HW pg 380
45-85 odd