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Unit 1: Introduction to Trigonometry

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Unit 1: Introduction to Trigonometry LG 1-1: Angle Measures LG 1-2: THE Unit Circle LG 1-3: Evaluating Trig Functions LG 1-4: Arc Length Quiz Thursday – PowerPoint PPT presentation

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Title: Unit 1: Introduction to Trigonometry


1
Unit 1 Introduction to Trigonometry
  • LG 1-1 Angle Measures
  • LG 1-2 THE Unit Circle
  • LG 1-3 Evaluating Trig Functions
  • LG 1-4 Arc Length
  • Quiz Thursday?
  • TEST MONDAY

2
Consider a circle, centered at the origin with 2
rays extending from the center.
One ray is fixed along the positive x-axis
The other can rotate about the center
  • These rays form an angle. The fixed ray is called
    the initial side of the angle.
  • The other side is called the terminal side.
  • Any angle with vertex at the origin and initial
    side along the positive x-axis is in standard
    position.

3
As the terminal side is rotated counterclockwise,
the measure of the angle that is formed
increases.
30o
135o
210o
4
The rotation of the terminal side may include 1
or more complete revolutions about the center.
The measurement representing 1 complete
revolution is 360o
1 revolution 360o
2 revolutions 720o
1 revolution 60o 420o
5
Angles that differ by one or more complete
revolutions are called coterminal angles.
  • For example 74o, 434o, and 794o are all
    coterminal angles. Why?
  • Think of at least 2 coterminal angles for 105o

6
The terminal side of an angle can also rotate
clockwise. A negative number is used to denote
these angle measures.
-45o
-150o
-420o
7
Suppose the angles on your cards are in standard
position. Place each angle in the quadrant that
contains its terminal side.
245o 275o 440o -94o
397o -240o 198o 945o
800o -32o 300o -210o
8
Suppose the angles on your cards are in standard
position. Place each angle in the quadrant that
contains its terminal side.
9
90o
-240o
397o
-210o
800o
440o
First, label the points where the circle
intersects the axes.
How would these angles change if they opened
clockwise?
180o
0o
360o
245o
-32o
198o
-94o
300o
275o
945o
270o
10
How do bulldogs get flat noses?
  • Complete the activity in the next 10 minutes. You
    may work with a partner (so you dont have to
    keep flipping!)

11
A unit other than degrees is also used to
describe the measure of an angle. It is called
the radian.
  • Suppose there is a circle with radius of 1
    centered at the origin. Its called the Unit
    Circle
  • Form an angle in standard position so that it
    intercepts an arc whose length is one unit.
  • The angle made is given the measurement of 1
    radian.

Approximately 6.28 of these slices can fit all
the way around the circle
12
  • You will convert degrees to radians and vice
    versa by using this conversion

13
Examples
  • Convert the following to degrees
  • B. Convert the following to radians
  • C. Determine which quadrant each of the above
    angles is located.

14
Practice
15
Ticket out the Door
  • On a half sheet of paper, describe in words what
    a coterminal angle is. How do you find a
    coterminal angle?

16
Homework
  • Complete the worksheet
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