Download Introduction to the Unit Circle

NAME:_____________________________________________
Topics in Pre-Calc II – Introduction to the Unit Circle
DATE:_________
PERIOD:_______
RECIPROCAL TRIG FUNCTIONS

SECANT is the reciprocal trigonometry function of _____________

COSECANT is the reciprocal trigonometry function of _____________

COTANGENT is the reciprocal trigonometry function of _____________
Secant
Cosecant
Cotangent
sec  =
csc  =
cot  =
cos  =
sin  =
tan  =
Exercise: Find the values of all six trigonometric functions of angle W given the diagram below
REFERENCE ANGLES
Examples:
Find the reference angle in each example below.
UNIT CIRCLE TRIGONOMETRY
Exercise: A line segment is constructed from the origin, intersecting the circle at
in Quadrant I, as shown.
The line segment makes an angle with the positive -axis. Label the angle above. Find an expression in terms
of and for
,
, and
.
UNIT CIRCLE PATTERNS
So we now know that any line segment starting at the origin
and making an angle with the -axis will
intersect the circle at the point
. This fact allows us to construct the unit circle, which shows
the sine and cosine ratios for special angles in all four quadrants.
 Recall the special right triangles to help fill out the table below
30
45
60
sin 
cos 

Can you identify any patterns that can help you memorize the unit circle? Write them below.
Exercise: Use the unit circle and trigonometric identities to evaluate the following expressions.
1.
(
)
2.
(
)
3.
(
)
4.
(
5.
( )
6.
(
)
10.
(
)
11.
( )
)
7.
8.
9.
12.
13.