1 / 14

Warm-Up Reading

Warm-Up Reading.

lauren
Download Presentation

Warm-Up Reading

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm-Up Reading When the German mathematician BartholomaeusPitiscuswrote 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.

  2. Weekly Learning Plan 2-3-14PreAPPrecalculus • 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 PreCalWorkshop – 7 am to 8 am • Friday – 2/7/14 • Test on Analytic Trigonometry - 5.1 to 5.3 (Identities) • Prepare for Section 5.5 - Solving Equations

  3. Objectives - Work with IdentitiesClose 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 133 - 14 - 22 (CD 1 in your book) • Page 131 - 74 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.

  4. 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 • cos(x)[tan(x) + cot(x)] = csc(x) • cos2(x) - 1 = 1 + sec(x) cos2(x)-cos(x)

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

  6. cos2(x) - 1 = 1 + sec(x)cos2(x)-cos(x)

  7. Section 5.2 Homework Q&A • Page 603 - 604 • 1,3,5,7 • 11,15,17 • 33,35 • 57, 59, 61

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

  9. 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) = ?

  10. Trigonometric Identities = 1 Quotient/Reciprocal Pythagorean Even - Odd Sum/Difference Double Angle Half Angle 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) • sin2(x) + cos2(x) =1 • 1 - sin2(x) = cos2(x) • 1 - cos2(x) = sin2(x) • tan2(x) + 1 = sec2(x) • cot2(x) + 1 = csc2(x) • sin(2x) = 2sin(x)cos(x) • cos(2x) = cos2(x) - sin2(x) • cos(2x) = 2 cos2(x) -1 • cos(2x) = 1 - 2 sin2(x)

  11. Page 614 - # 1 and 2 • Find sin(2 ) • Find cos(2 ) 5 3 4

  12. Page 614 - # 8 8. sin( ) = 15/17, and in Q2 Find sin(2 ) and cos(2 )

  13. Page 615 - #20 20.

  14. Homework Section 5.3 • Page 614 - Section 5.3 • 4, 5 • 7, 9 (only a and b) • 15, 17, 19 • Try #25

More Related