SECTION 3.7 TRIGONOMETRICPROOFS
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ACTIVITY: CONVERT THE FOLLOWING ANGLES INTO SUMSOR DIFFERENCES OF 30°, 45°, 60°, 90°, 180°, 270°, OR 360°
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I) PROVE:
Change the ratios:
Find all angles equal to
A.I. angles
Both angles are complimen-tary to
Relate each ratio
To angle “a” or “b”
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II) PROVE:
Change the ratios:
Find all angles equal to
Relate each ratio
To angle “a” or “b”
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Note: Sine functions are odd functions:
PROVE:
Cosine functions are even functions:
PROVE:
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The sum and difference identities can be used to findthe exact value when you sine/cosine angles that aresums or differences of special angles
It can only work with angles that are sums ordifferences of special angles: 30, 60, 90 and 45
EX: FIND EXACT VALUE WITHOUT A CALCULATOR:
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PRACTICE: FIND EXACT VALUE WITHOUT A CALCULATOR:
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Rationalize the denominator
PROVE THE FOLLOWING IDENTITY:
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Differenceidentity
Simplify
Formula Sheet
PRACTICE: PROVE
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Take thereciprocal
SumIdentity
Formula Sheet
PRACTICE: PROVE
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The reciprocal ofsec(x)  cos(x)
Formula Sheet
PROVE
Difference of squares
Pythagorean Identity
Difference Identity
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PROVE THE IDENTITY
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Quotient Identity
Sum Identity
Multiply allterms by:
Simplify
Quotient Identity
III) DOUBLE ANGLE IDENTITIES
Verify the identities Numerically with:
The identityis valid
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PROVING THE DOUBLE ANGLE IDENTITIES
To prove the Double Angle Identities, use the “Sum Identities”
Ex: Prove
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PRACTICE: PROVE THE FOLLOWING IDENTITIES
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PROOFS USING DOUBLE ANGLE IDENTITIES
Use the Double-Angle Identity
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PRACTICE: PROVE THE FOLLOWING IDENTITIES
Multiply top &bottom by:
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CHALLENGE: PROVE
Sum Identities
Use the Double Angle Identities
for  “sin2x”  &  “cos2x”
Expand/Distribute
Combine like-terms
Pythagorean Identity
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