Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference...
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Transcript of Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference...
![Page 1: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/1.jpg)
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Pre-CalculusChapter 5
Analytic Trigonometry
![Page 2: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/2.jpg)
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5.4 Sum & Difference Formulas
Objectives: Use sum and difference formulas to
evaluate trigonometric functions, verify identities, and solve trigonometric equations.
![Page 3: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/3.jpg)
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Consider This…. Determine whether each equation is
true or false. Justify your answer.
1cos30cos29cos.2
60sin14sin74sin.1
![Page 4: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/4.jpg)
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Sum & Difference Formulas Sine
Cosine
Signs are the same.
Signs change.
![Page 5: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/5.jpg)
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Sum & Difference Formulas Tangent
![Page 6: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/6.jpg)
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Example 1 Find the exact value of cos 75°.
Check your answer with a calculator.
![Page 7: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/7.jpg)
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Example 2 Find the exact value of .
12sin
![Page 8: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/8.jpg)
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Example 3 Simplify.
47tan152tan1
47tan152tan.2
80sin110cos80cos110sin.1
![Page 9: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/9.jpg)
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Example 4 Find the exact value of sin (u + v)
given
where and
where
5
4sin u
20
u
13
12cos v
v2
![Page 10: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/10.jpg)
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Example 5 Prove the cofunction identity.
xx sin
2cos
![Page 11: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/11.jpg)
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Example 6 Simplify each expression.
3tan.2
2
3cos.1
![Page 12: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/12.jpg)
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Example 7 Find all solutions of the equation in
the interval [0, 2π).
14
sin4
sin
xx
![Page 13: Chapter 5 Analytic Trigonometry 1. 5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify.](https://reader036.fdocuments.net/reader036/viewer/2022082713/5697bfb61a28abf838c9e28e/html5/thumbnails/13.jpg)
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Homework 5.4 Worksheet 5.4