• Law of Sines & Law of Cosines:
  • Final Exam Review: #7
  • WebWork: “Law of Sines” (Problems 3-6)
  • WebWork: “Law of Cosines” (Problems 1-3)
  • Patrick JMT videos: http://patrickjmt.com/the-law-of-sines-example-1/, http://patrickjmt.com/the-law-of-sines-example-2/, http://patrickjmt.com/law-of-cosines-example-5/

• Proving Trig Identities:
  • “Trigonometric Identities Worksheet” (handed out in class on Fri Dec 8, pdf available in Files; the exercises on the last 2 pages are due Wednesday)
  • Final Exam Review: #10
  • Trig textbook, Sec 1.4: Examples 2-4 (pp32-33)
  • Trig textbook, Sec 5.1: Examples 1 & 2 (pp212-213)
  • PatrickJMT videos: http://patrickjmt.com/proving-an-identity-example-1/ & http://patrickjmt.com/proving-an-identity-example-2/

• Solving Trig Equations (using the unit circle)
  • Final Exam Review #11
  • Quiz #8: question #2
  • WebWork: “SolvingTrigEquations” (Problems 1-7)
  • PatrickJMT video: http://patrickjmt.com/solving-trigonometric-equations/

Our final exam will be Monday, Dec 18 (at the usual class time, 10-11:40am).

The questions on the final exam will be very similar in format to the exercises on the Math Department’s Final Exam Review sheet:

MAT1275 Final Exam Review

(A hardcopy of the Final Exam Review sheet was handed out in class, and the pdf is also available online at http://www.citytech.cuny.edu/mathematics/docs/review/MAT1275FinalRview.pdf or on OpenLab: https://openlab.citytech.cuny.edu/groups/mat1275en-ganguli-fall2017/files/).

Note that many of the exercises on our midterm exams and quizzes were very similar in format to these exercises.  The best way to review for the final is to work through the Final Exam Review sheet, and study the related midterm exam solutions and quiz solutions as you do so.  All the midterm and quiz solutions are on OpenLab–download them!

Below is a guide to the exercises on the Final Exam Review sheet, with similar exam questions, WebWork exercises, and textbook examples listed for further review.

#1: Solving Quadratic Equations (using the quadratic formula)

• Quiz #3 (question #2)
• Quiz #4 (question #3)
• Exam #1 (question #3)
• WebWork: “QuadraticFormula” set

#2: Graphing Quadratic Functions (by completing the square to identify the vertex)

• “Graphing Quadratics” class handout (pdf available on OpenLab)
• Quiz #4
• Exam #2 (question #3)
• Exam #3 (question #1)

#3: Simplifying Complex Fractions (using least common denominators)

• Exam #2 (question #2)
• Exam #3 (question #6)
• WebWork: “ComplexFractions-Method1” set, Problem 6

#4: Graphing Circles (by completing the squares to identify the center and radius)

• Quiz #5 (question #1)
• Exam #2 (question #4)
• WebWork: “Circles” set, Problems 1-4

#5: Complex Numbers (multiplying via “FOIL”; dividing using the complex conjugate)

• Exam #2 (question #2)
• Quiz #8 (question #3)
• WebWork: “ComplexNumbers” set, Problems 5-8

#6: Solving a system of 3 linear equations in 3 variables

• Quiz #1
• Exam #1 (question #5)
• Algebra textbook, Sec 3.6: Example 1 (pp280-281)

#7: Solving systems involving nonlinear equations

• Exam #2 (question #5)
• Algebra textbook, Sec 9.4: Example 1(b) (p777), Example 4 (p779)

#8: Finding the values of the trig functions based on the value of one trig function (and information about the sign of one other trig function):

• Exam #3 (question #5)
• WebWork: “CoordinatePlaneTrig” set, Problems 4 & 5
• Trigonometry textbook, Sec 1.3: Example #5 (p26)

#9: Using the Law of Sines or Law of Cosines

• Exam #4 (TBD)
• Trig textbook, Sec 7.1: Example 1 (pp317-318)
• Sec 7.2: Examples 2 & 3 (pp331-332)

#10: Verifying Trig Identities–use the fundamental trig identities and algebra

• Exam #4 (TBD)
• Trig textbook, Sec 1.4: Examples 2-4 (pp32-33)
• Trig textbook, Sec 5.1: Examples 1 & 2 (pp212-213)

#11: Solving Trig Equations (using the unit circle)

• Exam #4 (TBD)
• Quiz #8 (question #2)
• WebWork: “SolvingTrigEquations” set (Problems 1-7)

#12: Solving an exponential equation (using logarithms):

• Exam #3 (question #3)
• Quiz #7 (question #1)
• Algebra textbook, Sec 8.7: Example 7 (p722)

#13: Evaluating logarithms (using the definition of logarithms)

• Exam #3 (question #2)
• Quiz #6 (questions #1(c) & #1(d))
• WebWork: “LogarithmicFunctions” (Problems 6-10)
• Algebra textbook, Sec 8.4: Examples 1 & 2 (pp682-683)