PreCalc 12/11 Unit 6 Trigonometry
Day 4 Notes
Tangent & Reciprocal Graphs
The tangent graph is unlike the two previous graphs we have looked at in some ways and
similar to it in other ways. Let’s have a closer look at it.
Ex 1
Graph one cycle of a tan graph
Maximum
Minimum
Domain
Range
Amplitude
Period
Phase Shift
Vertical Displacement
x-intercept
y-intercept
Asymptotes
Reciprocal Graphs
Just like in the previous unit on Transformations, we take the reciprocal of a graph by
making each y value transform into 1/y.
Matty 2014
PreCalc 12/11 Unit 6 Trigonometry
Ex 2
Domain
Day 4 Notes Page 2
Graph one cycle of the cosecant function (sin graph shown)
Range
Period
Asymptotes
It is important to note that all our other features (phase shift etc.) work exactly the same
as with the other graphs.
Ex 3
Domain
Graph one cycle of the secant function (cos graph shown)
Range
Period
Asymptotes
PreCalc 12/11 Unit 6 Trigonometry
Ex 4
Day 4 Notes Page 3
Graph one cycle of the cotangent function (tan graph shown)
Domain
Range
Period
Asymptotes
These graphs can all be stretched, compressed, reflected and shifted just like all the
others. Just the follow the rules from the last unit and you will be fine. In summary, our
six graphs look like this:
y = sin x
y = cos x
y = tan x
y = csc x
y = sec x
y = cot x
PreCalc 12/11 Unit 6 Trigonometry
Day 4 Notes Page 4