Day 1: Angles In Standard - PowerPoint PPT Presentation

1 / 9
About This Presentation
Title:

Day 1: Angles In Standard

Description:

Day 1: Angles In Standard Position terminal arm initial arm q terminal arm standard position non-standard position y y q q q x x initial arm 0 x y Positive angles ... – PowerPoint PPT presentation

Number of Views:43
Avg rating:3.0/5.0
Slides: 10
Provided by: PeterM179
Category:

less

Transcript and Presenter's Notes

Title: Day 1: Angles In Standard


1
Day 1 Angles In Standard Position
terminal arm
initial arm
standard position
non-standard position
terminal arm
q
q
q
initial arm 0º
2
y
Positive angles
ex 80º
rotate counterclockwise
q
x
3
Quadrants
90º
II
I
quadrant angle
I
II
III
IV
0º lt q lt 90º
180º

90º lt q lt 180º
180º lt q lt 270º
III
IV
270º lt q lt 360º
270º
4
Example
P(x, y)
Let P(x, y) be a point on the terminal arm of an
angle in standard position.
q1
Point P can be anywhere in the x-y plane.
q1 is in quadrant II.
90º lt q1 lt 180º
270º lt q2 lt 360º
q2
q2 is in quadrant IV.
P(x, y)
5
q3 180º
P(x, y)
q3
q3 lies in the negative x-axis.
6
The principal angle is the angle between 0º and
360º.
The related acute angle is the angle formed by
the terminal arm of an angle in standard position
and the x-axis.
q1
b
The related acute angle lies between 0º and 90º.
7
q
q
b
b
q 220º
b 220º 180º
q 150º
40º
b 180º 150º
30º
q 325º
b
b 360º 325º
q
35º
8
Example 1 The point P(5, 4) lies on the
terminal arm an angle in standard position.
a) Sketch the angle.
b) Determine the value of the related acute angle.
q
5
b
4
P(5, 4)
c) Determine the principal angle q.
q 180º 39º
q 219º
9
Example 2 The point P( 6, 7) lies on the
terminal arm an angle in standard position.
P(6, 7)
a) Sketch the angle.
b) Determine the value of the related acute angle.
7
q
b
6
c) Determine the principal angle q.
q 180º 49.4º
q 130.6º
Write a Comment
User Comments (0)
About PowerShow.com