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Mastering Trigonometric Integrals: Logical Problem-Solving Strategies

Explore essential strategies for integrating trigonometric functions, including recognizing patterns, applying substitution methods, and using power reduction formulas. Understand guidelines for evaluating integrals involving sine, cosine, secant, and tangent.

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Mastering Trigonometric Integrals: Logical Problem-Solving Strategies

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  1. Final Daily Quiz of 1st Quarter!!!!!! • 2. • 3.

  2. Essential Question

  3. Section 8.3 Trigonometric Integrals

  4. Mastering today’s topic is all about having a logical problem solving strategy and recognizing patters! Pro-Tip: Don’t try to memorize…just think about your goal!

  5. Example 1: (n Odd) Could you do this problem if the integral was a product of sine and cosine? Strategy: Factor out an even number of sin x and swap it for cos x (Pythagorean Identity). Then use u-substation to integrate. How would you go about integrating cosine to an odd power? Similarities/Differences?

  6. Example 2: (n Even) Strategy: Power Reduction Formula How would you go about integrating sine to an even power? Similarities/Differences?

  7. Example 3: ( m or n Odd) Could we get u-substitution to work for us? Strategy: Leave one sine/cosine and re-write the rest using the Pythagorean Identity. Then you can use u-substitution to integrate. If you have sinodd you re-write______. If you have cosodd you re-write______.

  8. Example 4: ( m and n Even) Will our strategy from the previous slide work? Strategy: Use Power Reduction Identities on BOTH trig functions.

  9. Example 5: Strategy: Product – Sum Formulas

  10. Example 6: What trigonometric functions “is friends” with cotangent?

  11. Example 7: What trigonometric functions “is friends” with tangent?

  12. Example 8: Strategy: Basic u-substation…don’t rush to judgement and overcomplicate things!

  13. Example 9: What trigonometric functions “is friends” with tangent? What trigonometric functions “is friends” with secant? Strategy: Create a situation when you can do a u-substitution with u = sec (x) and du=sec(x)tan(x).

  14. Guidelines for Evaluating Integrals Involving Sine and Cosine

  15. Guidelines for Evaluating Integrals Involving Secant and Tangent

  16. Homework Section 8.3 #5-17 odds, 33-41 odds, 43, 51, 67, 95

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