Warm-Up Reading When the German mathematician Bartholomaeus Pitiscus wrote Trigonometria, in 1595, the word trigonometry made its first appearance in print. However, Egyptian and Babylonian mathematicians used aspects of what we now call trigonometry as early as 1800 BC. The word trigonometry comes from two Greek words: trigon, meaning triangle and metron, meaning measure. Thus, trigonometry is the study of triangle measures. The definitions of the trigonometric functions on the unit circle are attributed to Swiss mathematician, Leonhard Euler.

Weekly Learning Plan PreAP Precalculus  Monday – 2/3/14 Quiz Results from Friday  Review of factoring, simplifying rational expressions Section 5.2 Homework Q/A Section 5.3 Introduction Double Angles  Tuesday – 2/4/14 Section 5.3 Continued - Introduction Half Angles Technology Exercise - Identity or Equation?  Wednesday - 2/5/14 Group Work Review HW from 5.2 and 5.3 to compare results Test Review - Identities - Section 5-1 to 5-3  Thursday 2/6/14 PreCal Workshop – 7 am to 8 am  Friday – 2/7/14 Test on Analytic Trigonometry to 5.3 (Identities) Prepare for Section Solving Equations

Objectives - Work with Identities Close gaps with prerequisite skills!  Quiz Results - Overall very good Most issues are as expected - factoring and working with rational expressions  Consider the following:  Extra Practice - You know if you need it! Page (CD 1 in your book) Page to 87, 88 to 97, 108 to 120 Warning: Simplifying trigonometric expressions and verifying identities can be a significant challenge for students whose algebraic manipulation skills are weak.

Section 5.1 Quiz  Do two-line proofs – explain your steps as you go, 10 points each 5 points for proof, 5 points for explanations of steps 1) cos(x)[tan(x) + cot(x)] = csc(x) 2) cos 2 (x) - 1 = 1 + sec(x) cos 2 (x)-cos(x)

cos(x)[tan(x) + cot(x)] = csc(x)

cos 2 (x) - 1 = 1 + sec(x) cos 2 (x)-cos(x)

Section 5.2 Homework Q&A  Page  1,3,5,7  11,15,17  33,35  57, 59, 61

Special Cases 57. sin(a) = 3/5, a in Q1 sin(b) = 5/13, b in Q2 Find sin(a+b), cos(a+b)

5.3 - Double Angle, Half Angles Think/Pair/Share: With a neighbor, find solutions to the following. 1. sin(x + x) = ? 2. cos(x + x) = ?

Trigonometric Identities Quotient/Reciprocal Pythagorean Even - Odd = 1 Sum/Difference Double Angle Half Angle sin 2 (x) + cos 2 (x) =1  1 - sin 2 (x) = cos 2 (x)  1 - cos 2 (x) = sin 2 (x) tan 2 (x) + 1 = sec 2 (x) cot 2 (x) + 1 = csc 2 (x) sin(x + y) = sin(x)cos(y) + cos(x)sin(y) sin(x - y) = sin(x)cos(y) - cos(x)sin(y) cos(x + y) = cos(x)cos(y) - sin(x)sin(y) cos(x - y) = cos(x)cos(y) + sin(x)sin(y) sin(2x) = 2sin(x)cos(x) cos(2x) = cos 2 (x) - sin 2 (x)  cos(2x) = 2 cos 2 (x) -1  cos(2x) = sin 2 (x)

Page # 1 and 2  Find sin(2 )  Find cos(2 ) 3 4 5

Page # 8 8. sin( ) = 15/17, andin Q2 Find sin(2 ) and cos(2 )

Page #20 20.

Homework Section 5.3  Page Section 5.3 4, 5 7, 9 (only a and b) 15, 17, 19 Try #25