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

2. Essential Question

3. Trigonometric Integrals
Section 8.3
Trigonometric Integrals

4. Trigonometry for Calculus BC
Poster by: Ananya Tripathi
Pythagorean Identities
Power-Reducing Formulas
Product-to-Sum Formulas
Sum and Difference Formulas
Double-Angle Formulas

5. 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!

6. 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?

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

8. Could we get u-substitution to work for us?
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______.

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

10. Product-to-Sum Formulas
Example 5:
Strategy: Product – Sum Formulas
Product-to-Sum Formulas

11. Pythagorean Identities
Example 6:
What trigonometric functions “is friends” with cotangent?
Pythagorean Identities

12. Pythagorean Identities
Example 7:
What trigonometric functions “is friends” with tangent?
Pythagorean Identities

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

14. What trigonometric functions “is friends” with tangent?
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).

15. Guidelines for Evaluating Integrals Involving Sine and Cosine

16. Guidelines for Evaluating Integrals Involving Secant and Tangent

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