Unit Circle Trig
TS: Making decisions after reflection and review
Warm Up:
Test your unit circle knowledge. You have 3 minutes.
(This is a generous amount of time for something that is supposed to be
memorized.)

 7 
cos 

4


tan  0 

 2 
sin 

 3 
cos  
 3 
tan 

2


 7 
cos 

6


 4 
tan 

3


sin  30
o
tan  225
o
Definition of Trig Functions
Let t be a standard position angle. If (x,y) is
a point r units from the origin.
y
sin t =
csc t =
(x,y)
r
cos t =
sec t =
tan t =
cot t =
x
The point (3, -9) is on the terminal side of
an angle in standard position. Determine
the exact values of the six trigonometric
functions of the angle.
What is the measure of the angle in degrees?
What Quadrant is θ in?
a) sin θ < 0
and cos θ < 0
b) sec θ > 0
and
cot θ < 0
c) tan θ > 0
and
csc θ < 0
Why is it important to know what quadrant
the angle is in anyway???
Find all six trig functions for the
11

standard position angle t =
6
Find all six trig functions for the
3

standard position angle t =
2
Trig functions are Periodic
sin(t  2 n)  sin t
cos(t  2 n)  cos t
tan(t   n)  tan t
Evaluate each using the period as an aid.
15
13
31
sin
cot
sec
2
4
6
 11 
csc  

6


sec2341
 13 
tan  

3


 7 
cos  

 6 
81
cos
4
1323
tan
2
Try using your unit circle trig skills to answer
the below word problem.
The monthly normal termperature T (in °F) for
Santa Fe, NM is given by
 t
7 
T  49.5  20.5cos   
6 6 
where t is the time in months, with t=1
corresponding to January. Find the monthly
normal temp for
a) Jan
b) July
c) Dec
a)29°F
b)70°F c)31.746°F