Transcript Angles, Degrees, and Special Triangles

Verifying Trigonometric Identities
MATH 109 - Precalculus
S. Rook
Overview
• Section 5.2 in the textbook:
– Verifying more complicated identities
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Verifying More Complicated
Identities
Verifying More Complicated
Identities
• Some guidelines to bear in mind:
– Pick the more complicated side as the starting point
• CANNOT switch back and forth between sides – pick
one side and stick with it until the end
– Cannot work with both sides because we have not
yet established an identity
– Look to apply Pythagorean Identities or manipulations
of them
• Helps to simplify the problem
– Apply algebraic operations such as multiplication or
addition/subtraction of fractions
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Verifying More Complicated
Identities (Continued)
– Rewrite trigonometric functions in terms of sines
and cosines
– Always remember the ending point
• Each step taken in a proof should lead towards the
ending point somehow
– Always try something! Even if the step does not
yield the desired result, it can be useful in another
way
• Success in proving identities will only come
with PRACTICE!!
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Verifying More Complicated
Identities (Example)
Ex 1: Verify the identity:
2
a) csc A  csc A sec A
cot A
b) sin1 2 x cos x  sin 5 2 x cos x  cos3 x sin x
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Verifying More Complicated
Identities (Example)
Ex 2: Verify the identity:
a) cos  cot   1  csc 
1  sin 
b) sec B  cos B  tan B sin B
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Verifying More Complicated
Identities (Example)
Ex 3: Verify the identity:
a) 1  sin x  cos x  2 sec x
cos x
b)
1  sin x
1
1

1
sin x  1 csc x  1
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Summary
• After studying these slides, you should be able to:
– Verify more complicated identities
• Additional Practice
– See the list of suggested problems for 5.2
• Next lesson
– Sum & Difference Formulas (Section 5.4)
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