1. Trigonometric Ratios & Pythagorean TheoremB
Mr. Halling
Algebra Prep Program
August 8, 2011 A C

2. DO NOW: Make a Histogram, Cumulative Frequency Histogram, and a Box-and-Whisker Plot using last year’s August Regents scores
56, 59, 65, 65, 66, 66, 66, 67, 68, 71, 72, 72, 73, 75, 76, 76, 84

3. Trigonometric Ratios What is trigonometry? What is SOH CAH TOA?
Introductory Video

4. Trigonometric Ratios
Ratios of the sides of a right triangle are called trigonometric ratios.
In ΔABC below, you see the relationships between the sides and angle A. A B C
Leg adjacent to A
Hypotenuse
Leg opposite A

5. Trig. Ratios SOH CAH TOA Introduce the transparency:
Sine = length of the opposite side
length of the hypotenuse
Cosine = length of the adjacent side
length of hypotenuse
Tangent = length of the opposite side
length of the adjacent side

6. Example Find the ratio for sin A, cos A, and tan A: Sin A = Cos A =B C 13 12 5

7. Example Find the sin B, cos B, and tan B: Sin B = Cos B = Tan B = 1312 5

8. Using the Calculator
When using SIN, COS, or TAN on the calculator, we simply hit the desired ratio and enter the measure of the angle
**WE MUST REMEMBER TO PUT THE CALCULATOR IN DEGREE MODE!
Hit MODE and scroll down to RADIAN and hit the arrow to the right to DEGREE

9. Working with Sine (SOH)
Find the measure of angle θ: 20 12

10. Working with Sine (2)
Find the measure of angle θ: 18 6

11. Working with Sine (3)
Find the measure of angle θ: 30 16

12. Working with Cosine (CAH)
Find the measure of angle θ: 41 16

13. Working with Cosine (2)
Find the measure of angle θ: 11 6

14. Working with Tangent (TOA)
Find the measure of angle θ: 16 11

15. Working with Tangent (2)
Find the measure of angle θ:
20.5
9.3

16. Groupwork
Work with a partner, a group, or by yourself to complete p.136#1-12
If you have any questions, ask myself or Mrs. Oakley
You may take a break once you have all the questions answered correctly and checked by Mr. Halling or Mrs. Oakley

17. The Pythagorean Theorem
Introduction
Overhead Projection

18. Find the missing side using the Pythagorean TheoremX 40 30

19. Find the missing side using the Pythagorean TheoremX 8 6

20. Find the missing side using the Pythagorean TheoremX 12 9

21. Find the missing side using the Pythagorean Theorem17 9 M

22. Find the missing side using the Pythagorean Theorem13 A 12

23. Find the missing side using the Pythagorean Theorem20 Y 7