Download Unit Circle Trig

Unit 1 day 3: Unit Circle Trig
Thinking Skill: making decisions after reflection and review
Warm Up:
1) The two gears below turn together. If the smaller gear’s radius is 5in and the larger gears radius is
1ft, how far does the larger gear turn (meaning what is the central angle) when the smaller gear turns
60°?
Definition of Trig Functions
Let t be a standard position angle. If (x,y) is a point r units from the origin.
sin t =
csc t =
cos t =
sec t =
tan t =
cot t =
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 standard position angle t =
11
6
Find all six trig functions for the standard position angle t =
3
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.
sec
13
6
cot
31
4
 13 
tan  

 3 
 11 
csc  

 6 
sec2341
cos
81
4
sin
15
2
 7 
cos  

 6 
tan
1323
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