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Weekly Trigonometry Plan: Identity Proving and Workshop Activities

This weekly plan outlines various activities and learning objectives centered around trigonometric identities. Starting with a review of fundamental concepts, students will participate in strategic group work emphasizing proven identity methods. Daily objectives include understanding identities, developing proving strategies, and engaging in guided practice and quizzes. Notable activities comprise group presentations, workshops, and individual quizzes designed to reinforce key trigonometric formulas and to practice two-line proofs, ensuring students can clearly explain each step in their reasoning.

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Weekly Trigonometry Plan: Identity Proving and Workshop Activities

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  1. Weekly Plan • Monday – 1/27/14 • Chapter Test Review – final thoughts • Introduction to Identities – Learning objectives • What is an identity? • What are the fundamental trigonometric identities? • Tuesday – 1/28/14 • Develop a useful strategy for proving identities • Work examples – “I do”, “We do” • Wednesday Group Work – (short day version) • “Y’all Do” - Work trig puzzles/make group presentations • Thursday PreCal Workshop – 7 am to 8 am • Friday – 1/24/14 • Special Topic – Why do we need to explain our steps? • Questions/Quiz on Section 5.1 – prove a couple of identities • Move on to Section 5.2 – Apply Sum/Difference Identities

  2. Q/A on Verifying Identities • Questions? • Guided Practice - as a group • Review on page 640 • Problems 1, 5, 9

  3. Page 640 - Problem 1 1. sec(x) - cos(x) = tan(x) sin(x)

  4. Page 640 - Problem 5 5. 1 - tan(x) = csc(x) - sec(x) sin(x)

  5. Page 640 - Problem 9 9. 1 - sin2(x) = cos(x) 1+cos(x)

  6. 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)

  7. Section 5.2 - Page 599Sum and Difference Formulas cos(x+y) = cos(x)cos(y) - sin(x)sin(y) cos(x-y) = cos(x)cos(y) + sin(x)sin(y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y) sin(x-y) = sin(x)cos(y) - cos(x)sin(y) • provides us a way to find exact values by using our standard reference values in our table!

  8. Remember this??? Rad. Deg. sin cos tan

  9. Examples: Page 603 4. cos 6. cos50ocos5o + sin50osin5o

  10. Examples: Page 603 • 10. Verify the following identity • cos(a-b) = cot(a)cot(b) + 1 • sin(a)sin(b)

  11. Special Cases 50. sin(x+h) - sin(x) = cos(x) sin(h) + sin(x) cos(h) -1 h hh

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

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

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