October 29, 2012
The Unit Circle is our Friend!
Warm-up: Without looking at your Unit Circle!
Determine: 1) The quadrant the angle is in; 2) The
reference angle; and 3) The sign of the sine and
cosine.
1. 300°
2. -135°
3. 2π/3
4. π/6
HW 4.4: Pg. 319 #30-36, 44-56, 82-86 all EVENS
Quiz last class on unit circle, trig functions, and reference
angles
Memorizing the unit circle!
• http://www.purposegames.com/game/unitcircle-quiz
Ms. PD! Don’t forget to show E
block how to use the reference
angle! It makes the unit circle
easier!
Lesson 4.4
Use the reference angle to help you find all
the points around the unit circle.
A reference angle is the acute angle formed by the
terminal side of θ and the x-axis.
75


For example, the reference angle of 225°
is 45°
.
64
6
4




6

5
6


Using the reference angle and quadrant to
help find the sine and cosine
• All you need to remember is the first quadrant
and the reference angle.
• Don’t forget about 0 and π/2!
Students
All
U
N
I
T
C
I
R
C
L
E
Take
Calc
Without referring to your notes, find the following:
(think of the reference angle and quadrant!)
1. sin (π/6)
2. cos (3π/4)
3. sin (5π/3)
4. cos (7π/6)
5. cos (3π/2)
6. sin (π)
7. sin (-2π/3)
8. cos (-5π/4)
Let’s go the other way around…
Find the two angles, θ, that has the following
trig function value.
1. sin θ = 1/2
2. cos θ = √3/2
3. cos θ = -1/2
4. cos θ = 1
5. sin θ = √2/2
6. sin θ = -√2/2
7. cos θ = -√3/2
8. sin θ = -1
Fundamental Trig Identities
Reciprocal Identities
1
sin  
csc 
1
csc  
sin 
Quotient Identities
1
cos  
sec 
1
tan  
cot 
1
sec  
cos 
1
cot  
tan 
sin 
tan  
cos 
Pythagorean Identities
sin2θ + cos2θ = 1
1+ tan2θ = sec2θ
1+ cot2θ = csc2θ
cos 
tan  
sin 
What about the other trig functions?
Find the value for each trig
function:
1. sec (π/4)
Find θ (2 angles) for the
following trig functions:
5. sec θ = 2
2. csc (3π/2)
6. cot θ = 1
3. tan (4π/3)
7. tan θ = √3
4. cot (7π/6)
8.
2 3
csc  
2
I have… Who has???
Which class is the fastest B or E? Extra
Halloween candy given to the winner on
Wednesday!