Unit Circle and the Coordinate Plane.notebook
April 25, 2017
Apr 20­1:56 PM
The Coordinate Plane and The Unit Circle
Unit Circle ­ a circle with its center at the origin and a radius of 1.
Sep 7­1:57 PM
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
New vocabulary:
θ
- (pronounced "theta"), a Greek letter often
used to designate an angle
Unit Circle - a circle whose radius has a length
of one unit and whose center is at the origin
Jan 30­7:06 PM
Unit Circle
(0,1)
(1,0)
(-1,0)
(0,0)
(0,-1)
Jan 30­6:51 PM
Unit Circle
Unit Circle and the Coordinate Plane.notebook
(0,1)
April 25, 2017
(x,y)
(0,y)
1
θ
(0,0)
y
(1,0)
x
(x,0)
Task:
Find Cos and Sin (0,-1)
Jan 30­6:51 PM
Unit Circle
(0,1)
(cosθ, sinθ)
1
θ
(-1,0)
(0,0)
(0,-1)
Jan 30­6:51 PM
y
(1,0)
x
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
Unit Circle
(0,1)
(cosθ, sinθ)
1
θ
(-1,0)
(0,0)
y
(1,0)
x
(0,-1)
Jan 30­6:51 PM
Unit Circle
(0,1)
y
1
θ
(1,0)
(-1,0)
-x (0,0)
(0,-1)
Jan 30­6:51 PM
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
Unit Circle
(0,1)
θ
-x
(-1,0)
(1,0)
(0,0)
-y
1
(0,-1)
Jan 30­6:51 PM
Unit Circle
(0,1)
θ
(-1,0)
x
(1,0)
(0,0)
1
(0,-1)
Jan 30­6:51 PM
-y
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
Unit Circle
(0,1)
Quadrant II
Quadrant I
(1,0)
(-1,0)
(0,0)
Quadrant IV
Quadrant III
(0,-1)
Jan 30­6:51 PM
Unit Circle
(0,1)
Students
Quadrant II
All
Quadrant I
cos <0
cos >0
sin >0
sin >0
(1,0)
(-1,0)
Take
(0,0)
Quadrant III
Calculus
Quadrant IV
cos <0
cos >0
sin <0
sin <0
(0,-1)
Jan 30­6:51 PM
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
The terminal side of <ROP in standard position intersects the unit circle at P(0.6,­0.8) . If the m<ROP is Θ find:
a) sin Θ
b) cos Θ
c) quadrant <ROP
O
R
1
P(0.6,­0.8)
Feb 2­7:55 AM
The terminal side of <ROP in standard position intersects the unit circle at P . If the m<ROP is Θ find:
a) sin Θ
b) cos Θ
c) quadrant <ROP
P
1
O
R
Feb 2­7:55 AM
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
The terminal side of <ROP in standard position intersects the unit circle at P . If the m<ROP is Θ find:
a) sin Θ
b) cos Θ
c) quadrant <ROP
P
1
R
O
Feb 2­7:55 AM
ex. Circle O is a unit circle. Given the coordinates of point P, find sin θ and cos θ.
b)
a)
O
A
O
A
P
P
(2
2 √2
__
P √ , ­___
P(­0.82, ­0.57)
Sep 7­2:17 PM
2
(
Unit Circle and the Coordinate Plane.notebook
April 25, 2017
For each given angle in standard position determine to the nearest tenth the coordinates of the point where the terminal side intersects the unit circle.
1) ­180 2) 137 3) 312
Jan 29­3:18 PM