Download 5.7 – Sketching the Reciprocal Trigonometric Functions Recall the

5.7 – Sketching the Reciprocal Trigonometric Functions
Recall the reciprocal graphing techniques used for sketching rational functions like the reciprocal
linear and the reciprocal quadratic functions from unit #2.
Ex.
if y = f(x)
then y = 1/f(x)
The same technique can be used to sketch the reciprocal trigonometric functions.
f(x) = sin θ
g(x) = cos θ
10
10
10
5
5
5
−π
π
2π
3π
4π
−π
−5
csc = cosecant
π
2π
3π
4π
−π
−5
sec = secant
−10
π
cot = cotangent
sec θ = 1/cos θ
10
5
5
5
2π
3π
4π
4π
3π
4π
cot θ = 1/tan θ
10
π
3π
−10
10
−π
2π
−5
−10
csc θ = 1/sin θ
Note that
these sketches
are to give
one a general
idea of the
shape and are
not exact as
have stretch
factors.
h(x) = tan θ
−π
π
2π
3π
4π
−π
π
−5
−5
−5
−10
−10
−10
2π
Use the accompanying sheets to accurately sketch the reciprocal trigonometric functions.
Once sketched describe the period, amplitude, domain, range, increasing and decreasing intervals
in the table below;
Function
sin θ
Increasing
Decreasing
csc θ
cos θ
sec θ
tan θ
cot θ
5.7 – sketching the reciprocal trigonometric functions
Domain
Range
Period
Amplitude
5.7 – Sketching the Reciprocal Trigonometric Functions Investigation Sheet
Have your sketches
from section 5.4 on top
of these functions so
you can take the
reciprocal of them.
Reciprocal Trigonometric Functions using degrees
1) f(x) = csc θ
8
Add decimal to
make y-axis
from -1 to 1
6
4
2
−270
−180
−90
90
180
270
360
450
540
630
720
90
180
270
360
450
540
630
720
90
180
270
360
450
540
630
720
−2
−4
−6
−8
10
2) g(x) = sec θ
8
6
4
2
−270
−180
−90
−2
−4
−6
−8
10
3) h(x) = cot θ
8
6
4
2
−270
−180
−90
−2
−4
−6
−8
10
5.7 – sketching the reciprocal trigonometric functions
5.7 – Sketching the Reciprocal Trigonometric Functions Investigation Sheet
Basic Trigonometric Functions using radians
1) f(x) = csc x
2) g(x) = sec x
3) h(x) = cot x
5.7 – sketching the reciprocal trigonometric functions