6.4 Values of Trigonometric
Functions
Definition: Let 
be a nonquadrantal
angle in standard position. The reference angle for 
is the acute angle 
that the terminal
side of 
makes with the x-axis.
Example 1: Find the reference angle 
for 
, and sketch 
and 
in standard position
on the same coordinate plane.
(a) 
(b) 
(c) 
(d) 
Theorem: If 
is a nonquadrantal
angle in standard position, then to find the value of a trig function at 
, find its value for the reference angle 
and prefix the
appropriate sign.
Example 2: Use reference angles to find
exact values of sine, cosine, and tangent of 
if
(a) 
(b) 
Example 3: Using a calculator find 
to the nearest 
if 
and 
.
Homework
assignment: 6.4 #1, 3, 5, 7, 9, 11, 13, 15,
17, 18, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 41