Verifying Trigonometric Identities
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Transcript Verifying Trigonometric Identities
Pre calculus Problem of the Day
Homework p. 578 1-21 odds
Simplify the following:
2 2
a) sin cos
6 6
2 2
b) sin cos
4 4
4 2 4 2
c) sin cos
3
3
Trigonometric Identities - a statement of equality that is
true for all values where the function is defined.
Reciprocal Identities:
1
sin
csc
1
cos
sec
1
tan
cot
1
csc
sin
1
sec
cos
1
cot
tan
Quotient Identities:
sin
tan
cos
cos
cot
sin
Pythagorean Identities:
Even/Odd Identities:
sin 2 cos2 1
sin sin
1 cot 2 csc 2
cos cos
tan 1 sec
2
2
tan tan
Verifying Trigonometric Identities
To verify a trigonometric identity we must show that one side of
the identity can be simplified so that it is identical to the other
side or each side can be simplified independently until they are
identical.
Never treat an identity like an equation. We are not solving
for the variable.
Techniques for verifying trigonometric identities.
1) Rename using the fundamental identities.
2) Rewrite a more complicated side in terms of sines and
cosines.
3) Factor.
4) Combine fractional expressions using an LCD.
5) Separate a single-term quotient into two terms.
6) Multiply the numerator and denominator on one side by a
binomial factor that appears on the other side of the
identity.
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