Download In this chapter we will use identities to... 1. Evaluate trig. functions, 2

November 20, 2014
Chapter 5 Analytic Trigonometry
Section 5.1 Using Fundamental Identities
Objectives: Use fundamental trig. identities to evaluate trig. functions
and simplify trigonometric expressions.
In this chapter we will use identities to...
1. Evaluate trig. functions,
2. Simplify trig. expressions,
3. Develop additional trig. identities,
4. Solve trig. equations
Review of Identities covered so far:
Reciprocal Identities
sin u =
csc u =
1
csc u
1
sin u
cos u =
1
sec u
tan u =
1
cot u
sec u =
1
cos u
cot u =
1
tan u
Quotient Identities
sin u
u
cot u = cos
sin u
tan u = cos u
Pythagorean Identities
sin2u + cos2u = 1
tan2u + 1 = sec2u
Cofunction Identities
sin (90˚ - u) = cos u
sec (90˚ - u) = csc u
cos (90˚ - u) = sin u
csc (90˚ - u) = sec u
1 + cot2u = csc2u
cot (90˚ - u) = tan u
tan (90˚ - u) = cot u
Even
Even/Odd
Odd Identities
sin (-u) = - sin u Odd tan (-u) = - tan u Odd sec (-u) = sec u Even
cos (-u) = cos u Even cot (-u) = - cot u Odd csc (-u) = - csc u Odd
Tip: For each one of these, there are 2 other versions that you
should be familiar with.
November 20, 2014
Ex1: If csc u = -5/3 and cos u > 0, find the values of the other five
trigonometric functions.
sin u = -3/5
cos u = 4/5
tan u = -3/4
s
c
Ex2: Find the value of tan u given that sec u = 2.
tan u = √3
Note: Could use Pyt
1 + tan2u =
Ex3: Simplify.
a) sec x - tan x sin x
b) csc2x cot x - cot x
c) tan x sin x + cos x
d)
sec t
tan t
1 + sec t
tan t
a)
cosx
b)
cot3x
c)
sec x
d)
cot t
November 20, 2014
Ex4: Factor the following trig. expressions.
a) cos2x - 1
a) (cos x +1)(cos x
b) sin2u - 3 sin u - 10
b) (sin u +2)(sin u
c) sec2t - tan t - 3
c)
Ex5: Rewrite sec 1x - 1 so that it is not a fraction.
(tan t + 1)(tan
Ex5: cot x csc x + co
Ex6: Use the substitution x = 3sin u, 0 < u < π/2, to express
√9 - x as a function of u.
2
Ex6:
Ex7: Is sec x sin3x + sin x cos x = tan x an identity?
Yes o
r
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