Section 4.4Trigonometric Functions
of Any Angle
Trigonometric Functions
of
Any Angle
Example
0
0
0
0
Evaluate the cosine function and the cotangent function
at the following four quadrantal angles:
a. =0 0
b. 902
c. =180
3d. =270
2
The Signs of the Trigonometric Functions
Example
Name the quadrant in which lies if the cotangent
is positive and the sine is negative.
Example
4Given that cot = and sin >0 find the following:
3sin =
cos =
sec =
csc =
Example
Find the reference angle, ', for each of the following
angles:
4
3
7
6
= - 120
Example
0
Find the reference angle, ', for each of the following
angles:
7
3
13
6
= 405
Evaluating Trigonometric Functions Using Reference
Angles
1
1
2
1
2
3
345
45 30
60
Find the sine, cosine and tangent of 30, 45 and 60 degree angles.
Here are the answers to the previous slide
Example
Use the reference angles to find the exact value of
each of the following trigonometric functions:
4sin
3
7cos
6
tan - 120
Example
0
Use the reference angles to find the exact value of
ech of the following trigonometric functions:
7sec
3
13csc
6
cot 405
(a)
(b)
(c)
(d)
0Find the reference angle for the angle -150
0
0
0
0
510
210
30
60
(a)
(b)
(c)
(d)
Use the reference angle to find the exact value of the
5following trigonometric function. csc
3
22
11
2
3
2
2 3
3