4.6 Graphs of Other Trigonometric Functions
Graph of y = tanx
x
0
π
6
π
4
π
3
5π
12
89π
180
1.57
π
2
y=tanx
Feb 13­11:42 AM
Tangent Curve:
Period:
Domain:
Range:
Vertical Asymptotes:
Points on the graph 1/4 and 3/4 between consecutive
asymptotes have y-coordinates 1 and -1
X-intercept:
Odd Function:
Feb 13­11:46 AM
1
Graphing Variations of y = tanx
y = A tan (Bx - C)
1.) Find two consecutive asymptotes by finding an interval containing one period.
2.) Identify an x‐intercept midway between the consecutive asymptotes.
3.) Find points on the graph 1/4 and 3/4 of the way between the consecutive asymptotes.
These points have y‐coordinates of A and ‐A.
4.) Use steps 1‐3 to graph one full period of the function
Ex. 1: Graph y = 2tan
x
2
for - π < x < 3π
Practice: Graph y = 3 tan 2x for
-π
4
<x<
3π
4
Feb 13­11:47 AM
π
Ex. 2 Graph two full periods of: y=tan (x + 4 )
π
Practice: Graph y = tan (x - 2)
Feb 13­11:47 AM
2
Cotangent Curve: y = cotx
Period:
Domain:
Range:
Vertical Asymptotes:
Points on the graph 1/4 and 3/4 between consecutive
asymptotes have y-coordinates 1 and -1
X-intercept:
Odd Function:
Feb 13­11:47 AM
Graphing Variations of y = cotx
y = A cot (Bx - C)
1.) Find two consecutive asymptotes by finding an interval containing one period.
2.) Identify an x‐intercept midway between the consecutive asymptotes.
3.) Find points on the graph 1/4 and 3/4 of the way between the consecutive asymptotes.
These points have y‐coordinates of A and ‐A.
4.) Use steps 1‐3 to graph one full period of the function
Ex 3: Graph y = 3cot2x
1
π
Practice: Graph y = 2 cot 2 x
HW: pg 546 6-12 EVEN, 18-24 EVEN
Feb 13­11:48 AM
3
Graph each function.
1. y= 2tan (x-π)
2. y = cot x +1
Mar 18­8:39 AM
4