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Math 41
Final Exam Review
5.1 Using Fundamental Identities & 5.2 Verifying Trig Identities
You need to know the
fundamental trig identities:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
cot
)
cot(
sec
)
sec(
csc
)
csc(
tan
)
tan(
cos
)
cos(
sin
)
sin(
Identities
Even/Odd
sec
2
csc
csc
2
sec
tan
2
cot
cot
2
tan
sin
2
cos
cos
2
sin
Identities
Cofunction
csc
cot
1
sec
tan
1
1
cos
sin
Identities
n
Pythagorea
sin
cos
cot
cos
sin
tan
Identities
Quotient
tan
1
cot
cos
1
sec
sin
1
csc
cot
1
tan
sec
1
cos
csc
1
sin
Identities
Reciprocal
2
2
2
2
2
2

=

=


=


=

=


=

=

=

=

=

=

=

=
+
=
+
=
+
=
=
=
=
=
=
=
=
π
You need to be able to use these trig identities to find the values of all 6 trig functions
given one or two of them.
You need to be able to simplify a trig expression using these
identities.
In these sections, you need to be able to verify a trig identity.
If the question
asks you to verify, prove, or show
, that means that you pick one side and work with it
until you get the other side.
You are not allowed to work with both sides as if it were an
equation!!!!
No crossmultiplying both sides, no adding or subtracting expressions from
both sides, and no dividing both sides by trig functions!!!
Usually, if you are asked to
prove an identity that contains fractions, get a common denominator and then expand the
numerator.
You usually will be able to make a trig substitution in the numerator.
If all
else fails, try converting everything to sines and cosines.
Sometimes, if you only have
one fraction that contains single powers of sine and/or cosine, you can multiply both top
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 Fall '07
 BRUNSDEN,VICTORW
 Math, DoubleAngle Formulas, HalfAngle Formulas

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