Download 5.3 Trig Functions on the Unit Circle Unit Circle: Circle of radius 1

n
5.3 Trig Functions on the Unit Circle
Unit Circle: Circle of radius 1.
(x,y)
1
y
θ
x
sinθ =
cscθ =
cosθ =
secθ =
tanθ =
cotθ =
Dec 4­7:01 PM
Examples: Use the unit circle to
find each value.
1.) sin 90o
2.) cot(-180o)
Dec 4­8:03 PM
1
3.) cos(-270o)
4.) csc180o
Dec 4­8:04 PM
Special Triangles...
this is all you need to memorize.
45o
60
1
o
√2
1
2
45o
30o
√3
30-60-90 Triangle
1
45-45-90 Triangle
Dec 4­8:08 PM
2
Examples: Use the unit circle to
find the values of the six trig
functions for each angle.
1.) 225o
Dec 4­8:06 PM
2.) 120o
Dec 4­8:10 PM
3
3.) 330o
Dec 4­8:11 PM
(x,y)
r
y
θ
x
r = √ x 2 + y2
sinθ =
cscθ =
cosθ =
secθ =
tanθ =
cotθ =
Dec 4­8:14 PM
4
Examples: Find the values of the
six trigonometric functions for
angle θ in standard position if a point
with the given coordinates lies on its
terminal side.
1.) (-4,-3)
Dec 4­8:26 PM
2.) (5,-3)
Dec 4­8:28 PM
5
More Examples
1.) If cosθ <0, where would the
terminal side of the angle be located?
Dec 4­8:30 PM
Suppose θ is an angle in standard
position whose terminal side lies in
the given quadrant. For each
function, find the values of the six
trig functions for θ.
2.) cosθ= 12, Quadrant III
13
Dec 4­8:32 PM
6
3.) secθ = √3 , Quadrant IV
Dec 4­8:35 PM
Dec 6­7:07 AM
7