Day2.UnitCircle.17.notebook
January 13, 2017
Topic: Trig Functions
Aim: What is the UNIT CIRCLE and how can
we represent trig functions on the unit circle?
Do Now: Name the Quadrant in which each
angle lies:
1) 250 o
2) -250o 3) 330 o 4) -120o
IV
II
III
III
Jan 10­8:28 PM
Def: A unit circle is a circle with its center
on the origin and has a radius of 1 unit.
C
y
( , )
A
sinθ=
θ
O
x
B
D
s=o
h
cosθ=
c=a t=o
h
a
Jan 10­8:33 PM
1
Day2.UnitCircle.17.notebook
January 13, 2017
Point is on the unit circle whose center is the origin. If θ is an angle in standard position whose terminal ray passes through point A, what is the value of a) sinθ b) cosθ
y
A
θ
x
Jan 10­8:45 PM
Fill in the blanks with sinθ or cosθ
(cosθ , sinθ)
tanθ= sinθ
cosθ
Jan 10­8:54 PM
2
Day2.UnitCircle.17.notebook
January 13, 2017
Name the line segment that represents:
sinθ
y
C
cosθ
D
θ
tanθ
O
A
B
x
Jan 10­9:02 PM
Circle O is a Unit Circle
y
II
I
(­x,y)
O
(x,y) (cosθ, sinθ)
tan
θ= sinθ
x
cosθ
(x,­y)
(­x,­y)
III
IV
Jan 11­4:55 PM
3
Day2.UnitCircle.17.notebook
January 13, 2017
S
A
sin
positive
All positive
T
C
cos positive
tan positive
Jan 11­5:04 PM
Angles in standard position that have the
same terminal side are called coterminal
angles.
Ex 1) Are 300o and -60o coterminal angles?
y
x
To find coterminal angles
add or subtract multiples of 360o
Jan 9­9:56 PM
4
Day2.UnitCircle.17.notebook
January 13, 2017
2) Find the smallest positive angle
coterminal with each of the following:
a) 430o
b) -240o
c) 780o
Jan 9­9:59 PM
Jan 13­11:24 AM
5