Math 120 Notes 8.3 – Special Values of the Trig Functions
I.
Special Triangles
A.
B.
C.
Evaluate the 6 trig functions at each of the following angles.
1.

4
2.

6
3.

3
Evaluate the following without using a calculator.
1.
4 cos 45  2 sin 45
2.
1  tan2 30  csc2 45
3.
cot
Use the calculator to evaluate the following. Round to three decimal places.
1.
II.


 cos
4
6
cos 28
2.
cot

14
Application
A rain gutter is to be constructed of aluminum sheets 12 inches
wide. After marking off a length of 4 inches from each edge, this
length is bent up at and angle  as shown in the diagram.
(a)
Express the area A of the opening as a function of .
(b)
Find the area of the opening for  = 30°,  = 45°,
 = 60°, and  = 75° (use the calculator only for the last
computation).
(c)
Graph your area formula from (a). Find the angle  that
makes the largest area. Thus, you will find the bending
angle that will allow the most water to flow through the gutter.