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

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

Trigonometric Ratios What is trigonometry? What is SOH CAH TOA? Introductory Video http://www.youtube.com/watch?v=NeIm_aSFd3I

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

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

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

Example Find the sin B, cos B, and tan B: Sin B = Cos B = Tan B = 13 12 5

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

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

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

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

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

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

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

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

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

The Pythagorean Theorem Introduction http://www.youtube.com/watch?v=Oa2rCxNTN6Y&feature=related Overhead Projection

Find the missing side using the Pythagorean Theorem X 40 30

Find the missing side using the Pythagorean Theorem X 8 6

Find the missing side using the Pythagorean Theorem X 12 9

Find the missing side using the Pythagorean Theorem 17 9 M

Find the missing side using the Pythagorean Theorem 13 A 12

Find the missing side using the Pythagorean Theorem 20 Y 7