3.4: Unit Circle Coordinates and Even/Odd Functions
Fill in the missing sides of the triangles and find the 3 trig ratios:
sin 60 =
sin 30 =
1
o
30
60o
cos 30 =
tan 30 =
1
30
2x
60 90
o
60
x
sin 45 =
30o
1
cos 60 =
tan 60 =
45o
cos 45 =
tan 45 =
o
45
What points do we use for 0o, 90o, 180o, 270o, and 360o when trying to figure out sine & cosine? Questions to ponder:
What is sin 70o ?
What is the range of sin and cos ?
Is (‐3, 4) on unit circle? Using unit circle...
b) cos
a) sin 150o
You will have to memorize the following coordinates: quadrantal angles multiples of 30 (denominator of 6)
multiples of 60 (denominator of 3) multiples of 45 (denominator of 4)
c) tan
(hint: duck n dog)
( , )
Unit Circle : radius = ___ rad
___ rad
___ rad
___ rad
___
( , ) ___ rad
___o
___ rad
___o
___o
___o
___ rad
___o
___ rad
___o
o
___o
___o ___ rad
( , )
___o ___ rad
___o
___o
___ rad
___o
___o
___o
___ rad
___ rad
___o
___o
___ rad
( , )
___ rad
___ rad
___ rad
( , )
Without the unit circle in front of you...
1. think reference angle / 2. write the point (cos , sin) / 3. make sure the sign (+/‐) is correct
a) cos
b) sec 225o
c) tan "EVEN" function: f(‐x) = f(x) vs. "ODD" function: f(‐x) = ‐f(x)
cos(­x) = sin(­x) = tan(­x) = a) sin
Find the exact value without calculator. c) tan (‐180o)
b) cos Find all values of θ that make the equation true in the indicated interval. 3.4: 1-49 odd
#1‐29 odd
‐ for every problem write out the coordinate point before you write the answer.
‐ try NOT to use unit circle paper, but use the unit circle idea (coordinate points)
ex
a
r
t