1 8.3 Trigonometric Identities In this section, we will study the following topics: o Using trig...
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Transcript of 1 8.3 Trigonometric Identities In this section, we will study the following topics: o Using trig...
1
8.3 Trigonometric Identities
In this section, we will study the following topics:
o Using trig identities and algebra to simplify trigonometric expressions
o Verifying trigonometric identities
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Use the fundamental trig identities to simplify the following trigonometric expressions.
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12.tan 1x
Simplifying Trig Expressions
1. cos tan
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3. cot cos2
x x
2cos4.1 sin
Simplifying Trig Expressions
Use the fundamental trig identities to simplify the following trigonometric expressions.
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sin( )5.cos( )
x
x
2 26. cos sec 1
Simplifying Trig Expressions
Use the fundamental trig identities to simplify the following trigonometric expressions.
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Simplifying Trig Expressions
2sin 17.
tan sin tan
Use the fundamental trig identities to simplify the following trigonometric expression.
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Verifying Trig Identities Algebraically
Goal: Get one side of the equation equal to the other!
Strategy:
Hold one side of the equation constant
Transform one side of the equation into the other using the trig identities. Look for:
Reciprocal identities
Quotient identities
Pythagorean identities
Even/Odd Identities
When you have successfully verified the identity, write Q.E.D. at the end.
Quod erat demonstrandum = “Which was to be proven”
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Verifying Trig Identities Algebraically
HELPFUL HINTS:
1. Only work with ONE SIDE OF THE EQUATION AT A TIME. Do not use inverse operations!(i.e. do not ‘move’, multiply, or divide terms from both sides of the equation.)
2. You usually try to SIMPLIFY THE MORE COMPLICATED SIDE. Leave the other side alone.
3. When other options are not available, you can CHANGE ALL TERMS INTO EXPRESSIONS CONTAINING SINE AND /OR COSINE. Then simplify.
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Verify the trigonometric identity: csc tan sec
Verifying Trig Identities Algebraically
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Verify the identity:
csc2
csctan
Verifying Trig Identities Algebraically
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Verify the identity:2 2sec tan tan
cos sinsec
Verifying Trig Identities Algebraically
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Verify the identity:
cossec tan
1 sin
Verifying Trig Identities Algebraically
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Verify the identity:
Verifying Trig Identities Algebraically
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Verify the identity:
Verifying Trig Identities Algebraically
End of Section 8.3
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