9/17/04
(Fr)

Chapter 6.1 - Angles and their Measure

• Convert degrees, minutes, seconds and decimal forms of angles.
• Find arclength
• Convert degrees and radians
• Find linear speed of a rotating object

Lab Activity - To help students understand the relationship between linear distance and arclength, we completed a "circle lab".

Students are given a circular object such as a plate, a can, or a lid from a butter dish. Groups of students measure and record the radius. After measuring the radius, the object is rolled one complete revolution. The distance the object moves is measured and recorded. All groups report their findings and a stat plot of the data is made. A discussion of the slope in which all units divide out occurs. We soon find the C = 2πr is a specific case of S = θr where the angle 2π is one complete revolution of a circle. The next activity helps to explain why the units of 2π are called radians.
A circle is drawn on the board. Two students measure and mark the radius on a piece of rope. The piece of rope is then placed around the circle and the length of the radius becomes the arclength around the circle. A line is placed at the end of each length of the rope. It is determined that it takes approximately 6-1/3 lengths of the radius to go around the circle. Hence, the term radian is the angle which has its radius equal to its arclength. It takes 2π radians to complete one revolution of the circle.

The image at the left shows a circle with the radius measured and marked around the outside edge of the circle. Each of the blue numbers is the radian measure of the angle.

Assignment 6.1 / 1, 3, 4, 6, 7, 8, 11, 13, 16, 17, 23, 37, 40, 41, 45, 50, 54, 55, 61, 62, 67, 68, 74, 76, 77, 78, 86

9/20/04
(Mo)

Warmup 6.1 Graph the angle 240° to radians and graph. Convert the angle (11Π/3) to degrees and graph. With the RPM's found using the photogate, what is the linear speed of the bicycle wheel? How many RPM's must the wheel turn to travel at 15 mph?

Chapter 6.2 - The Unit Circle

• Find exact value of trig functions using the unit circle.
• Find the exact value of 30-45-60-90 degree angles.
• Use a calculator to approximate the trig values.

Assignment 6.2 / Complete the Unit Circle Chart, Trig Value Chart, and #'s 1, 4, 11, 12, 15, 24, 25, 53-66

9/21/04
(Tu)

Warmup 6.2

Without using your charts/graphs:

1. Draw a reference triangle at 150^o and find the six trig functions.
2. Find the six trig functions of the point (2/3, sqrt(5)/3) on the unit circle.
3. Draw the reference triangle for 11Π/3 and find the six trig functions.

Chapter 6.3 - Properties of Trig Functions

• Determine domain, range, period and signs of trig functions.
• Use identities to find value of trig functions
• Use odd-even properties to find exact values of trig functions

Assignment 6.3 / Complete Trig Rules Chart, 1, 6, 11, 12, 17, 20, 23, 24, 25, 30, 33, 38, 43, 44, 46, 49-51, 63, 64,

9/22/04
(We)

Warmup 6.3 -

1. Find the exact value of cos(11π/4) - sin(135°)
2. If tan θ = 4/3 and cos θ < 0, find the other five trig functions.

Chapter 8.1 / Right Triangle Trigonometry

• Find the value of trig functions of acute angles.
• Use the Complementary (Cofunction) Rules to find trig functions.
• Solve right triangles and applied right triangle problems.

Assignment 8.1 / 1, 4, 6, 9, 11, 14, 18, 22, 23, 29, 32, 38, 39, 42, 46, 50, 51, 58

9/23/04
(Th)

Warmup 8.1

1. Simplify sin 40^o + tan 40^o sin 50^o
2. Find the six trig functions.
3. A hot air balloon is tethered by a rope. From a point 226m from the tether, the angle of elevation is 58.3^o. What is the height of the hot air balloon?

Chapter 6.4 - Graphs of Sine and Cosine

• Graph sine and cosine functions using transformations.

Assignment 6.4 / 17, 19, 20, 21, 22, 24-27, 29, 31

9/24/04
(Fr)

Warmup 6.4 - Sketch and find D:, R:, Pd, Amp, Phase Shift

1. f(x) = 3sin(x)
2. f(x) = cos(2x) - 1
3. f(x) = (1/2)sin(x-π/2)

Chapter 6.5 - Graphs of Secant, Cosecant, Tangent and Cotangent

• Relate graphs of tangent and cotangent to slope.
• Relate graphs of secant and cosecant to cosine and sine.
• Graph each function using transformations.

Assignment 6.5 / 15, 18, 19, 21, 23, 26, 29, 31, 34 Find the D:, R:, Amp, Pd and phase shift where possible.

Warmup 6.5

1. Find the 6 trig functions of the angle to the point (-2, 3).
2. Construct a reference triangle and find the 6 trig functions for 5π/3.
3. If cos(θ) = -3/4 and tan(θ) < 0, find the csc(θ)
4. Use a calculator to find sin(115^o) and sec(3π/7).
5. Sketch (without grapher) f(x) = 3sin(2x) and f(x) = csc(x-π/4) + 2

Chapter 6.6 - Sinusoidal Function Fitting

• Fit a sine or cosine model to sinusoidal graphs or data.
• Explain the meaning of the mathematical model

Demo: Lincoln Average Temperature, Motion Detector on Wheel

By moving a motion detector around the radius of a wheel, the distance from the floor to a point on the wheel is measured. The sinusoidal function in the background represents the change in height over time. By fitting a model to the data, various attributes of the wheel can be determined including the radius, angular velocity, height of the center of the wheel and the position of the wheel when data collection started.

Assignment 6.6 - Fit data collected/provided in class. Part I

9/28/04
(Tu)

6.6 Warmup A

Fitting data part II.

Using the calculator for find a sinusoidal regression. Explaining the meaning of the regression values.

9/29/04
(We)

6.6 Warmup B - The distance to a wave is measured from a pier. If the distance varies from 4 ft to 16 ft. There are 8 waves in 2 minutes passing under the pier. Write and equation for the distance the wave is from the pier starting when the wave is closest to the pier.

Chapter 6 Review

Assignment 6.R / 3, 6, 9, 21, 24, 27, 37, (44, 45, 49, 53, 54, 62 Sketch and find D:, R:, Amp, Pd), 72, 73, 76

9/30/04
(Th)

10/1/04
(Fr)