Test #1, Thursday, February 4, Day 9, on sections 5.1-5.7.

Test #2, Tuesday, March 2, Day 16, on sections 6.1-6.5.

Test #3, Thursday, April 15, Day 26, on sections 7.1, 7.2, 7.5, 3.3, 3.4, 10.1-3 and earlier material.

SI meetings in BR 200 at 5:00 PM on Thursdays and at 3:30 PM on Mondays. Please take the time to see Chuck if your schedule permits. I think this can really benefit you.

Thursday, January 7, Day 1: Cover section 5.1 Angles and Their Measure. Top

• Discuss angles, degree measure, radian measure (q = s/r) and conversion of angle measure.
• Applications: Example 6, length of circular arc (s = rq ). Example 7, linear speed (Speed = s/t).
• In class homework examples: 5, 7, 10, 13, 25, 30, 87, and 96.
• Homework: 31, 32, 33, 40, 71, 74, 80, 82, 88, 95, 97, 102. Due 1/12/99. Remarks on homework #1.

Tuesday, January 12, Day 2: Cover section 5.2 Right Triangle Trigonometry. Top

• Discuss the six trigonometric functions, special triangles (45^o, 30/60^o), trigonometric identities, evaluating trigonometric functions with a calculator.
• Applications: Examples 7, 8 and 9, solving right triangles (include an inverse function solution).
• In class homework examples: 2, 6, 9, 13, 18, 28, 39b, 59, 65.
• Homework: 3, 8, 14, 17, 25, 29, 41, 60, 66, 67, 69, 79. Quiz #1 1/14/99. Remarks on Quiz #1

Thursday, January 14, Day 3: Cover section 5.3 Trigonometric Functions of Any Angle. Top

• Define "Trigonometric Functions of Any Angle"
• Define "Reference Angle" and determine the reference angles associated with various positive, negative, and oblique angles given in radian and degree measure.
• Define a periodic function. Which trigonometric functions are even?
• In class homework examples: 2, 10, 12, 15, and 61.
• Homework: 4, 9, 11, 13, 14, 21, 22, 40, 60, 62, 93, and 98. Due 1/19/99. Remarks on homework #2.

Tuesday, January 19, Day 4: Cover section 5.4 Graphs of Sine and Cosine Functions. Top

• Sketch the graphs of the basic sine and cosine functions by hand, noting the five key points (intercepts, minimum, maximum) in a period.
• Define amplitude, period, and phase shift and determine their values from the general equation.
• Determine horizontal and /or vertical translation.
• Use a trigonometric function to model data.
• In class homework examples: 6, 10, 16, 18, 26, 40, 83, 87.
• Homework: 3, 31, 33, 39, 41, 48, 50, 61, 63, 74, 80, 89. Quiz #2 1/21/99. Remarks on Quiz #2

Thursday, January 21, Day 5: Cover section 5.5 Graphs of Other Trigonometric Functions. Top The first SI meeting is today in BR 200 at 5:00 PM. The second SI meeting is Monday in BR 200 at 3:30 PM. Please take the time to see Chuck if your schedule permits, I think this can really benefit you.

• Graphs of the tangent, cotangent and reciprocal functions.
• Analyze and recognize the hills and valleys of a trigonometric function and its reciprocal on the same coordinate axis.
• Damped trigonometric graphs, analyzing a damped curve.
• In class homework examples: 2, 4, 38, 46, 50, 73.
• Homework: 6, 8, 18, 40, 45, 49, 56, 63, 64, 67, 68, 74. Due 1/26/99. Remarks on homework #3.

Tuesday, January 26, Day 6: Cover section 5.6 Inverse Trigonometric Functions. Top

• Definitions of inverse trigonometric functions, their domain and range.
• Using the inverse properties.
• Applications: Compositions of functions and some problems from Calculus.
• In class homework examples: 1, 5, 10, 24, 28, 55.
• Homework: 2, 3, 6, 11, 26, 32, 46, 56, 68, 71, 72, 74, 78. Take Home Quiz #3. Due on or before 2/2.

Thursday, January 28, Day 7: Cover section 5.7 Applications and Models. Top

• Right triangles
• Directions and bearings
• Harmonic motion
• In class homework examples: 14, 16, 32, 64
• Homework: 9, 12, 15, 17, 18, 23, 28, 34, 46, 61, 64. Homework #4 due 2/2.

Tuesday, February 2, Day 8: Review. Top

• Focus on concepts page 472
• Chapter 5 review exercises are divided into 21 sections, work at least one problem from each section.

Thursday, February 4, Day 9: Test #1.Key 1a Key 1b Top

Tuesday, February 9, Day 10: Cover section 6.1 Using Fundamental Identities. Top

• Use fundamental trigonometric identities to evaluate trigonometric functions and to solve trigonometric equations.
• Use fundamental trigonometric identities to simplify trigonometric expressions and to develop additional trigonometric identities.
• Use a graphing utility to demonstrate trigonometric identities.
• In class homework examples: 6, 15, 24, 45, 87.
• Homework: 8, 10, 16, 22, 23, 32, 50, 66, 70, 73, 80, 84. Quiz #4 on 2/11.

Thursday, February 11, Day 11: Cover section 6.2 Verifying Trigonometric Identities. Top

• The key to verifying identities and solving equations is the ability to use the fundamental identities and the rules of algebra to rewrite trigonometric expressions.
• Five guidelines for verifying Trigonometric Identities:

1. Work with one side of the equation at a time.
2. Look for opportunities to factor, add fractions, square a binomial or otherwise simplify.
3. Look for natural pairs of functions so you can apply fundamental identities: sines and cosines, secants and tangents, cosecants and cotangents.
4. As a last resort, convert all functions to sines and cosines.
5. Try something! Most discoveries are the result of analyzing failed initial attempts.

• In class homework examples: 5, 12, 22, 27, 61.
• Homework: 2, 6, 7, 16, 17, 25, 30, 36, 43, 54, 67, 68. Homework #5 due 2/16.

Tuesday, February 16, Day 12: Cover section 6.3 Solving Trigonometric Equations. Top

• Using standard algebraic techniques such as collecting like terms and factoring, isolate the trigonometric function then solve.
• Squaring and converting to quadratic type.
• Functions of multiple angles.
• Using inverse functions.
• In class homework examples: 3, 14, 33, 61.
• Homework: 2, 12, 32, 35, 36, 44, 60, 63, 64, 65, 66. Quiz #5 on 2/18.

Thursday, February 18, Day 13: Cover section 6.4 Sum and Difference Formulas. Top

• Derivation and application of sum and difference formulas.
• Use the difference formula to prove a cofunction identity, Example 5.
• Derive reduction formulas, Example 6.
• Derive a formula for the angle between two lines.
• In class homework examples: 2, 5a, 18, 25, 34, 42.
• Homework: 3, 4, 5, 6, 10, 14, 17, 24, 36, 38, 40, 44. Homework #6 due 2/23.

Tuesday, February 23, Day 14: Cover section 6.5 Multiple Angle and Product Sum Formulas. Top

• Multiple angle formulas of the form sin ku and cos ku, Examples 1-3.
• Product formulas of the form sin² u as power reduction formulas, Example 5.
• Half-angle formulas, sin (u/2), Examples 6 and 7.
• Products of the form sin u cos u and sum-to-product formulas, Examples 8, 9 and 11.
• In class homework examples: 2, 4, 27.
• Homework: 6, 8, 20, 28, 50, 53, 93, 94, 100. Homework #7 due on or before 2/25.

Thursday, February 25, Day 15: Review. Top

Tuesday, March 2, Day 16: Test #2. Key 2a Key 2b Top

Thursday, March 4, Day 17: Cover Section 7.1 The Law of Sines. Top

• To solve a triangle we need three pieces of information, one of which is a side.
• The Law of Sines, you must know at least one side and its opposite angle.
  In any tiangle with angles A, B, C and corresponding lengths of opposite sides a, b, c,
  (sin A)/a = (sin B)/b = (sin C)/c.
• In class homework examples: 4, 6, 22, 36.
• Homework: Enjoy your spring break March 6-14.

Tuesday, March 16, Day 18: Cover section 7.2 The Law of Cosines. Top

• The Law of Cosines can be used to solve the triangle given three sides (SSS), or two sides and their included angle (SAS).
  Let A be the angle included by sides b and c, with side a being opposite the included angle A, then
  

  a2 = b2 + c2 -2bc cos A;

  cos A = (b2 + c2 - a2)/2bc

• In class homework examples: 8, 20, 29, 38.
• Homework: Section 7.1 #2, 8, 14, 23, 30, 40, 41,
  Section 7.2 #6, 16, 19, 22, 26, 30, 36. Quiz #6 on 3/18.

Thursday, March 18, Day 19: Cover section 7.5 DeMoivre's Theorem. Top

• The absolute value of the complex number z = a + bi is given by
  |a + bi| = sqrt(a²+b²).
• The trigonometric form of a complex numberz = a + bi is
  z = r(cos q + isin q)
  where a = r cos q, b = r sin q, r = sqrt(a²+b²), and tan q = b/a.
• Multiplication and Division of Complex Numbers
• DeMoivre's Theorem
  If z = r(cos q + i sin q) is a complex number and n is a positive integer, then
  zⁿ = [r(cos q + isin q)]ⁿ = rⁿ(cos nq + isin nq).
• In class homework examples: 47, 72, 84.
• Homework: 10, 20, 30, 40, 50, 54, 76, 77, 84, 85, 99, 100. Quiz #7 on 3/23.

Tuesday, March 23, Day 20: Cover section 3.3 Real Zeros of Polynomial Functions. Top

• Long Division of Polynomials
• Synthetic Division, a shortcut for long division of polynomials by divisors of the form x - k.
• The Remainder and Factor Theorems
  If a polynomial f(x) is divided by x - k, the remainder is r = f(k).
  A polynomial f(x) has a factor (x - k) if and only if f(k) = 0.
  This remainder r is significant in the following ways:
  1. The remainder r gives the value of f at x = k.
  2. If r = 0, (x - k) is a factor of f(x).
  3. If r = 0, (k, 0) is an x-intercept of the graph of f.
• The Rational Zero Test
• Bounds for Real Zeros of Polynomial Functions
• In class homework examples: 30, 58, 80
• Homework: 8, 24, 37, 46, 56, 57, 58, 68, 76, 78, 96. Homework #8 due 3/25.

Thursday, March 25, Day 21: Cover section 3.4 The Fundamental Theorem of Algebra. Top

• The Fundamental Theorem of Algebra
  If f(x) is a polynomial of degree n, where n > 0, f has at least one zero in the complex number system.
• Linear Factorization Theorem
  If f(x) is a polynomial of degree n, where n > 0, f has precisely n linear factors
  f(x) = a_n(x - c₁)(x - c₂)...(x - c_n)
  where c₁, c₂, ..., c_n are complex numbers and a_n is the leading coefficient of f(x).
• Complex zeros occur in Conjugate Pairs
• Factors of a Polynomial: a quadratic factor with no real zeros is said to be irreducible over the reals.
• In class homework examples: 20, 30, 42
• Homework: 3, 5, 6, 19, 21, 22, 32, 33, 37, 39. Quiz #8 on 3/30.

Tuesday, March 30, Day 22: Cover section 10.1 Sequences and Summation Notation.

• An infinite sequence is a function whose domain is the set of positive integers.
  The function values a₁, a₂, a₃, a₄, . . . , a_n, . . . are the terms of the sequence.
• Factorial Notation
• Summation Notation and Properties of Sums
• In class homework examples: 10, 26, 54
• Homework: Enjoy your Easter Vacation April 1 - 4.

Tuesday, April 6, Day 23: Cover section 10.2 Arithmetic Sequences. Top

• A sequence is arithmetic if the differences between consecutive terms are the same. This number, d, is the common difference.
• The nth term of an Arithmetic Sequence
• The Sum of a Finite Arithmetic Sequence
• In class homework examples: 8, 18, 38
• Homework: Section 10.1 #9, 11, 25, 27, 53, 55
  Section 10.2 #7, 9, 17, 19, 29, 33, 55, 65. Quiz #9 on 4/8.

Thursday, April 8, Day 24: Cover section 10.3 Geometric Sequences. Top

• A sequence is geometric if the ratios of consecutive terms are the same.
  a₂/a₁ = r, a₃/ a₂ = r, . . . , a_n+1/a_n = r, r not zero.
  This ratio, r, is the common ratio.
• The sum of a geometric sequence
• Applications
• In class homework examples: 8, 18, 38
• Homework: 7, 9, 17, 19, 22, 30, 37, 66, 68 Homework #9 due 4/13.

Tuesday, April 13, Day 25: Review. Sample Questions for Test #3 with solutions, Top

Thursday, April 15, Day 26: Test #3.Key 3a Key 3b Top

Tuesday, April 20, Day 27: Cover section 10.4 Mathematical Induction. Top

• The Principle of Mathematical Induction Sample Proof Blank Proof Sheet
  Let P_n be a statement involving the positive integer n. If
  1. P₁ is true, and
  2. the truth of P_k implies the truth of P_k+1, for every positive k,
  then P_n must be true for all positive integers n.
• Sums of Powers of Integers
• Pattern Recognition
• Finite Differences
• In class homework examples: 6, 56
• Homework: 1, 2, 3, 7, 8, 22, 30, 32, 58, 60 Homework #10 due 4/22.

Thursday, April 22, Day 28: Cover section 10.5 The Binomial Theorem. Top

• Binomial Coefficients
• Pascal's Triangle
• Binomial Expansions
• In class homework examples: 8, 14, 54
• Homework: 1, 2, 3, 13, 17, 25, 43, 46, 66 Quiz #10 on 4/27.

Tuesday, April 27, Day 29: Lab. Top

• Lab due on 4/29.

Thursday, April 29, Day 30: Review. Top

by Jack Tompkins