Transcript 5.2: Verifying Trigonometric Identities

5.2: Verifying
Trigonometric
Identities
Identity
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An equation that is true for all real values
in the domain of the variable
sin x  1  cos x
2
2
Verify the Trigonometric Equation
tan  cos  sin 
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Guidelines for Verifying
Trigonometric Identities
Work with one side of the equation at a time. It is often
better to work with the more complicated side first.
Look for opportunities to factor an expression, add fractions,
square a binomial, or create a monomial denominator
Look for opportunities to use the fundamental identities.
Note which functions are in the final expression you want.
Sines and cosines pair up well, as do secants and tangents,
and cosecants and cotangents
 If the preceding guidelines do not help, try converting all
terms to sines and cosines
 ALWAYS TRY SOMETHING!
 THERE CAN BE MORE THAN ONE WAY! (TRY TO BE
EFFICIENT!)
Verify Trigonometric Identities
sec 2   1
2

sin

2
sec 
Combining Fractions Before Using
Identities
1
1

 2 sec 2 
1  sin  1  sin 
Verifying a Trigonometric Identity
(tan x  1)(cos x  1)   tan x
2
2
2
Converting to Sines and Cosines
tan x  cot x  sec x csc x
Rationalizing the Denominator:
Using Conjugates
1

1  cos x
Verifying Trigonometric Identities
cos y
sec y  tan y 
1  sin y
Working with Each Side Separately
2
cot 
1  sin 

1  csc 
sin 
tan x  tan x sec x  tan x
4
2
2
2
sin x cos x  (cos x  cos x) sin x
3
4
4
6
Homework
Page 365-367
2-10 even, 31-49 odd, 63
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