Sec 52a Prove the algebraic identity We begin by writing down the lefthand side LHS and should e nd by writing the righthand side RHS Each of the e xpressions between should be easily seen ID: 311514
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Slide1
Proving Trigonometric Identities
Sec.
5.2aSlide2
Prove the algebraic identity
We begin by writing down the left-hand side (LHS), and should
e
nd by writing the right-hand side (RHS). Each of the
e
xpressions between should be easily seen to be equivalent toits preceding expression…Slide3
General Strategies I
1. The proof begins with the expression on one side of
the identity.
2. The proof ends with the expression on the other side.
3. The proof in between consists of showing a
sequence of expressions, each one easily seen to beequivalent to its preceding expression.
Since “easily seen” can be a relative phrase, itis usually safer to err on the side of including too
many steps than too few!!!Slide4
Prove the algebraic identitySlide5
Prove the algebraic identitySlide6
Prove the trigonometric identitySlide7
General Strategies II
1. Begin with the more complicated expression and
work toward the less complicated expression.
2. If no other move suggests itself, convert the entire
expression to one involving
sines and cosines.3. Combine fractions by combining them over acommon denominator.Slide8
Tell whether or not is an identity:
Yes!!! is an identity!!!Slide9
Tell whether or not is an identity:
This is a phase shift of
of
the cosine function!
…which is the sine function!!
Yes!!! is an identity!!!Slide10
Combine
and Simplify:
How can we support this work
graphically
?Slide11
Guided Practice
: Prove the given identity.Slide12
Guided Practice
: Prove the given identity.Slide13
Guided Practice
: Prove the given identity.Slide14
Guided Practice
: Prove the given identity.Slide15
Guided Practice
: Prove the given identity.Slide16
Guided Practice
: Prove the given identity.Slide17
Guided Practice
: Prove the given identity.