The 7-4 to 7-6 Quiz is available until Wednesday, February 25th at midnight. There is no time limit and you may take the quiz a maximum of two times. The quiz consists of 10 questions on the following material.

• Lesson 7-4
  • Convert between rectangular and polar coordinates.
  • Convert between rectangular and polar equations.
• Lesson 7-5
  • Determine whether two vectors are equivalent.
  • Solve vector addition applications.
  • Solve applied problems involving horizontal and vertical components of vectors.
• Lesson 7-6
  • Find the component form and length of vectors.
  • Perform calculations with vectors in component form.
  • Express a vector as a linear combination of unit vectors.
  • Express a vector in terms of its magnitude and its direction.

Intro

In Lesson 7-6 we are learning about vector operations – basically the math involved with vectors. We’ll address questions like how we multiply, add, or subtract, or find the angle between two vectors.

Please memorize the operations defined in the blue boxes, as this will help you understand the material and will make the homework go more smoothly! Make sure you understand the concepts as you go through the worksheet and fill in the blanks.

Objectives

1. Perform operations with vectors in component form.
2. Express a vector as a linear combination of unit vectors.
3. Express a vector in terms of its magnitude and direction.
4. Find the angle between two vectors using the dot product.
5. Solve Applied Problems involving force.

Assignment

1. Read the introduction, objectives, and assignment.
2. Watch the section video found in Chapter Contents.
3. Read over the lesson and use to fill out the 7-6: Vector Operations Worksheet (Click Here to download the 7-6 Worksheet).
4. Complete the homework assignment.
5. Send the worksheet answers to my email or submit the filled out 7-6 worksheet to my box by Wednesday.

Intro

Lesson 7-5 is on vectors and their applications. Vectors are very important for Physics, which all of you will be taking next year! Vectors are used to measure quantities that require both a numerical value, like length or speed, and a direction. For example, Force is a vector because it involves a numerical value (the amount of force being applied) and a direction (the angle at which the force is being applied). If you push a lawnmower, the force vector you exert on the lawnmower depends on how hard you are pushing the lawnmower as well as the direction in which you are pushing.

Objectives

• Understand that vectors are made up of both a magnitude  (length) and direction.
• Determine whether two vectors are equivalent.
• Find the sum, or resultant, of two vectors.
• Resolve a vector into its horizontal and vertical components.
• Solve applied problems involving vectors.

Assignment

1. Read the introduction, objectives, and assignment.
2. Watch the section video found in Chapter Contents.
3. Read over the lesson and use to fill out the worksheet (click here to download the worksheet).
4. Complete the homework assignment.
5. Send the worksheet answers to my email or submit the filled out worksheet to my box by Wednesday.

Objectives

• Graph points given their polar coordinates.
• Convert from rectangular to polar coordinates and from polar to rectangular coordinates.
• Convert from rectangular to polar equations and from polar to rectangular equations.
• Graph polar equations.

Learning Materials

 Instructor Video:

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The 7-1 to 7-3 Quiz is available through Friday, January 30th. You will have 45 minutes and may take the quiz a maximum of two times. The quiz consists of 10 questions on the following material.

• Use the law of sines and the law of cosines to solve triangles.
• Graph complex numbers and find the absolute value of complex numbers.
• Convert between trigonometric notation and standard notation for complex numbers.
• Multiply and divide complex numbers in trig notation.

Lesson 2-2: Complex Numbers

Objectives

• Add, subtract, multiply and divide Complex Numbers in standard form.
• Simplify powers of i.
• Find the conjugate of a complex number.

Learning Materials

2-2 Instructor Video:

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7-3: Complex Numbers in Trigonometric Form

Objectives

• Graph complex numbers.
• Given a complex number in standard form, find trigonometric, or polar, notation; and given a complex number in trigonometric form, find standard notation.
• Use trigonometric notation to multiply and divide complex numbers.
• Use DeMoivre’s theorem to raise complex numbers to powers.

Note: You do not have to find roots of complex numbers.

Learning Materials

• 7-3 Power Point
• Chapter Contents ->Lesson 7.3 ->7.3 Video Lecture
• Chapter Contents -> Lesson 7.3 -> 7.3 Multimedia Textbook Section

I have a cough and am not going to be able to make an instructor video for this section, so please study the lesson using the materials above. The power point is what I would have done in a video, but without audio.

Objectives

• Know when to use the Law of Cosines (SAS and SSS triangles)
• Use the law of cosines to solve triangles.
• Determine whether the law of sines or the law of cosines should be applied to solve a triangle.

Learning Materials

7.2 Instructor’s Video:

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Objectives

• Know when to use the law of sines (to solve AAS, ASA and SSA triangles).
• Know that there can be zero, one, or two solutions for a SSA triangle.
• Use the law of sines to solve triangles.
• Find the area of any triangle given the lengths of two sides and the measure of the included angle.

Study Materials

• Video on Solving Triangles using the Law of Sines:

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• Video on the Area of an Oblique Triangle:

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Quiz 1: Chapter 5

To help you review for your end-of-semester exam, I have prepared 2 quizzes that may be taken a maximum of 2 times each. The quizzes may be taken in any order.

So study for the quiz, take it once, go back and study what you missed, and then take the quiz again if you need to. Only the final take will count for a grade. The exam will be comprehensive over Chapters 5 and 6.

Objectives

• Determine the six trigonometric ratios for an acute angle of a right triangle. (5.1)
• Given one function value, find the other five. (5.1)
• Determine trigonometric values for angles of 30, 45, and 60 degrees. (5.1)
• Find the function values of the complement of an angle given the function values of the angle. (5.1)
• Solve right triangles given certain information. (5.2)
• Solve angle of elevation/depression problems (5.2)
• For a given angle, find its coterminal angles and its complement and supplement. (5.2)
• Find function values given the coordinates of a point on the terminal side of the angle. (5.3)
• Use reference angles to find trigonometric function values. (5.3)
• Find an angle given a trigonometric function value and quadrant restriction. (5.3)
• Find points given in radian measure on the unit circle. (5.4)
• Find coterminal angles, complements, and supplements of angles given in radian measure. (5.4)
• Convert between radian and degree measure. (5.4)
• Find arc lengths and central angles (5.4)
• Find amplitude, period, & phase shift of sine & cosine functions, & use them to graph the functions. (5.6)

Make sure to memorize…

• The basic trig function values of an acute angle (defn of sine, cosine, etc.) (5.1)
• Co-function identities (5.1)
• Trig functions of any angle (5.3, pg 463)
• Converting between degree and radian measure (5.4)
• Defn of radian measure (pg 482)
• Defn of amplitude, period, phase shift (see pg 516 for a review)

Quiz 2: Lessons 6.1 – 6.2

Objectives

• Simplify and manipulate expressions containing trigonometric expressions. Be able to factor using the GCF, FOIL, and Difference of two squares. (6.1)
• Use the sum and difference identities to find function values. (6.1)
• Use cofunction identities to find function values and derive other identities. (6.2)
• Use double-angle identities to find function values. (6.2)
• Use half-angle identities to find function values. (6.2)
• Simplify trigonometric expressions using the double-angle and half-angle identities. (6.2)

Make sure to memorize…

• Pythagorean Identities
• Sum and Difference Identities for Sine and Cosine
• Cofunction Identities
• Double-Angle identities for sine and cosine

Objectives

• Solve Trigonometric Equations using exact values for 30, 45, and 60 degree angles and angles with 30, 45 or 60 degree reference angles.
• Solve Trigonometric Equations using your calculator for other angle measurements.

Lesson Overview

We are skipping lesson 6.4 for now – we will come back to it later. In this lesson you are solving trigonometric equations. The difference between solving trigonometric equations and proving trigonometric identities is that identities are always true statements – so we can prove them for any x-value. Solving trigonometric equations, however, involves finding the specific x-values that make the statement true.

Think back to the good old Algebra days. An example of an “Algebra Identity” would be 2x = 2x. This is an always true statement. It works for any x-value. On the other hand, the equation 2x +5 = 9 is not always true. It is only true for a specific value of x (x = 2, to be exact).

So in this lesson you are solving equations like our 2x + 5 = 9, but adding in the trig element. Here are a few things to keep in mind when solving problems:

• If a trig equation is quadratic, factor or use the quadratic equation (Examples 5, 6, 7)
• If a trig equation involves more than one function (sine and cosine, for example), see if you can use identities to re-write the equation in terms of only one function (Examples 9 – 11)

Study Materials

Video 1: Intro and Basic Examples (Examples 1 & 2)

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Video 2: Solving for “2x” and using your calculator (Examples 3 & 4)

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Video 3: Pythagorean Examples (Examples 5 – 7)

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