Objective: For students to learn how to prove identities. Standards: F-TF 8 HW: Worksheet 5.1...
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Transcript of Objective: For students to learn how to prove identities. Standards: F-TF 8 HW: Worksheet 5.1...
![Page 1: Objective: For students to learn how to prove identities. Standards: F-TF 8 HW: Worksheet 5.1 Proving Identities, Textbook section 5.1 problems Assessment:](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649ef65503460f94c094e9/html5/thumbnails/1.jpg)
• Objective: For students to learn how to prove identities.
• Standards: F-TF 8• HW: Worksheet 5.1 Proving Identities,
Textbook section 5.1 problems• Assessment: Observe understanding during
guided practice
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5.1 Identities
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Warm-up
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Identity
• An equation that is true for all its x values is called an identity.
• The equations in the warm-up are called identities.
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Why do we need to learn identities in trigonometry?
• They make things simpler.
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• In order to show an equation is an identity, we need to prove it. We will be practicing that a lot for the next few class periods.
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Let’s start with these…
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Reciprocal Identities
• True by definition
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Ratio Identities
• Use the right triangle definitions of sine and cosine to show that tan(x) = sin(x)/cos(x) and that cot(x) = cos(x)/sin(x)
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Pythagorean Identities
• Again, use right triangle definitions to show that sin2(x) + cos2 (x) = 1
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• Now let’s prove the other two Pythagorean identities.
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The 10 Commandments of Identities
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#1 Memorize the 8 Fundamental Identities.
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#2 NEVER CROSS AN EQUAL SIGN!!
Prove: tan(x)csc(x) = sec(x)
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#3 Try breaking up fractions with sum or differences in the numerator
Period 6 stopped here
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#4 Usually better to start on the more complicated side
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#5 Try adding and subtracting fractions by getting a common denominator
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#5 Try adding and subtracting fractions by getting a common denominator
Per 3 ended here after day 2
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#6 If you can distribute something, try
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#6 If you can distribute something, try
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#7 Try factoring
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#7 Try factoring
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#8 Try multiplying by a form of 1
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#8 Try multiplying by a form of 1(Pythagorean Conjugates)
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#8 Try multiplying by a form of 1
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#8 Try multiplying by a form of 1
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#9 Last resort, convert everything to sines and cosines.
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#9 Last resort, convert everything to sines and cosines.
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#10 - It is perfectly okay to give up at any point and start again with a new approach.
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HW
• P. 243: 9, 13, 17, 21, 25, 29, 33, 37