chapter five: analytic trigonometry the fundamental
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Chapter Five: Analytic Trigonometry
5.1 Using Fundamental Identities
The Fundamental Trigonometric Identities include:
Reciprocal Identities
1
sincsc
uu
1
cossec
uu
1
tancot
uu
1
cscsin
uu
1
seccos
uu
1
cottan
uu
Quotient Identities
sin
tancos
uu
u
coscot
sin
uu
u
Pythagorean Identities
2 2sin cos 1u u 2 21 tan secu u 2 21 cot cscu u
Co-function Identities
sin cos2u u
cos sin
2u u
tan cot
2u u
csc sec2u u
sec csc
2u u
cot tan
2u u
Even/Odd Identities
sin sinu u cos cosu u tan tanu u
csc cscu u sec secu u cot cotu u
Using only these identities we can do a lot with trig functions.
Examples: Use the given values to evaluate (if possible) all six trig functions.
1. 3 3
tan , cos3 2
x x
2. 3 3 5
sec , csc2 5
Ex: Simplify the trigonometric expression.
1. tan cscx x
2. 21 cos cscx x
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