1 8.3 Trigonometric Identities In this section, we will study the following topics: o Using trig...

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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



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sin( )5.cos( )

x

x

2 26. cos sec 1



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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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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


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Verify the identity:

csc2

csctan


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Verify the identity:2 2sec tan tan

cos sinsec


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cossec tan

1 sin


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End of Section 8.3

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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...