Trigonometric Functions Of General Angles Worksheet Template

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Section 7.4 – Trigonometric Functions of General Angles
In this section we will find the values of the trig functions of non-acute
angles. We do this by placing the vertex of the angle at the origin and
its initial side along the positive x-axis. Then we let the point (a, b)
represent some point on the terminal side of the angle . Using the
 
2
2
 
d
x
x
y
y
Distance Formula
, where (x
, y
) is
1
1
2
1
2
1
2
2
2
2
d
a
0
b
0
a
b
the origin (0,0) and (x
, y
) is the point (a, b), we have:
. We call the distance
2
2
from the origin to the point (a, b) the radius, r. Then we define the six trigonometric functions of  as shown in the
figure below (assuming no denominators are zero – if the denominator is zero then the function is undefined!).
Example 1: A point on the terminal side of an angle  is given. Find the exact value of each of the six trigonometric
functions of .
a) (-1, -2) First find r. Then, since we know a = -1 and b = -2, use these values with r to find the trig functions of .
 
1
3
,
b)
 
 
2 2
7.4
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