Trigonometry 29B

1
Trigonometry 2-9B

• Transformations on Graphs of Tangent, Cotangent,
• Secant and Cosecant

2
Transformations on other trigonometric graphs
cot x and tan x
csc x and sec x
A vertical stretch/shrink
A amplitude
B horizontal stretch/shrink, divide the critical
points by B.
C vertical shift, center line
D phase shift, add D to all new critical
points after effect from B.
Two cycles
Three cycles
3
Ex1. Graph y -5 3cot4x
divide asymptotes by 4
no phase shift
center line -5
stretch by 3
the curve happens up (down) 3 from the center
4
Ex2. Graph y 1 4sec18?
-5, 5, 15, 25
divide asymptotes by 18
no phase shift
center line 1
amplitude 4
5
-12, -6, 0, 6, 12
divide asymptotes by
phase shift -2
-14, -8, -2, 4
center line -3
amplitude 4