FST Chapter 4 - Circular Functions

SECTION 4-1 Measures of Angles and Rotations

Homework: p. 237 #2,3,5-15,19-22 & LM

New Terms:

FST Chapter 4 - Circular Functions

  1. draw an angle and label the angle, sides and vertex
  1. revolution
  1. radian
  1. draw a full turn, half turn, and quarter turn

FST Chapter 4 - Circular Functions

Questions to be answered by student during reading:

  1. Using Example 1, explain how to find two ways to find other radian measures equivalent to any given rotation.
  1. Copy the table of equivalent measures on p. 234

Deg / 0 / 30 / 45 / 60 / 90 / 120 / 135 / 150 / 180 / 360
Rad
Rev
  1. What conversions can be used to convert from

FST Chapter 4 - Circular Functions

  1. Degrees to radians
  1. Degrees to revolutions
  1. Revolutions to radians

FST Chapter 4 - Circular Functions

  1. 1 radian=______degrees
  1. Draw in the measures from #2 above on your copy of the unit circle.

Teacher Examples:

FST Chapter 4 - Circular Functions

  1. Draw a circle and rays showing a rotation of radians.
  1. Give 3 other radian measures, at least one “negative”, showing the same rotation as teacher example #1.

FST Chapter 4 - Circular Functions

FST Chapter 4 - Circular Functions

  1. Convert 31.4159 radians to degrees.
  1. Convert to radians.
  1. Convert to revolutions.

FST Chapter 4 - Circular Functions

FST Chapter 4 - Circular Functions

  1. How many revolutions equals radians?
  1. Convert to revolutions.

FST Chapter 4 - Circular Functions

SECTION 4-2 Lengths of Arcs and Areas of Sectors

Homework: p. 242 #1-4, 11-15 & LM

Reading Questions:

FST Chapter 4 - Circular Functions

  1. Give the formula for finding the Arc Length of a sector using degree measures.
  1. Show the proof for the Arch Length Formula in radians.
  1. Describe a sector of a circle.
  1. Give the formula for finding the Area of a Sector using degree measures.

FST Chapter 4 - Circular Functions

Formulas:

FST Chapter 4 - Circular Functions

Circular Arc Length
Circular Sector Area

FST Chapter 4 - Circular Functions

Teacher Examples:

  1. Find the length of an arc of a central angle with measure in a circle with radius 5 cm.
  1. Find the area of a 27 degree sector of a circle with radius 10 feet.
  1. Earth travels around the sun in an elliptical orbit, but one that is nearly circular with radius 93,000,000 miles. Using the circular approximation, about how far does the Earth travel in a single day. Use 365.25 days for the length of a year.


Section 4-3 Sines, Cosines, and Tangents

In Class Activity: Complete Activity on pg. 244

HW Problems: 1-4, 6-10, 13, 14, 15-19 & LM

Definitions/Theorems:

FST Chapter 4 - Circular Functions

  • Cosine
  • Sine
  • Unit circle:
  • (cosΘ, sinΘ)
  • Tangent = tanΘ
  • Sketch of the Unit circle

FST Chapter 4 - Circular Functions

Fill in the table with the appropriate information. See pg 247. This is a YARF.

Θ / Quadrant / cosΘ / sinΘ / tanΘ
0< Θ <Π/2
Π/2< Θ <Π
Π< Θ <3Π/2
3Π/2< Θ <2Π

Teacher Examples:

  1. Evaluate the following:

FST Chapter 4 - Circular Functions


FST Chapter 4 - Circular Functions

  1. Determine whether each value is positive (+ve) or negative (-ve).

FST Chapter 4 - Circular Functions