5.5. Frequency and Period of Sinusoidal Functions http://www.ck12.org
40 =^2 bπ→b= 20 π
f(x) =− 8 ·cos(π
20 x)
+ 6
Notice how the labeling on the graph is extremely deliberate. On both thexandyaxes, only the most important
intervals are labeled. This keeps the sketch accurate, evenly spaced on your paper and easy to read.
- The labeling is the most important and challenging part of this problem. The amplitude is 1. The shape is a
negative cosine. The vertical shift is 2. The period is^28 π=π 4. Working with this small period may be challenging
at first, but remember that halving fractions is as simple as doubling the denominator. - The amplitude is 3. The shape is a negative cosine. The period is^52 πwhich implies thatb=^45. The vertical shift
is 1.f(x) =− 3 ·cos(^45 x)+1.
Practice
Find the frequency and period of each function below.
1.f(x) =sin( 4 x)+ 1
2.g(x) =−3 cos( 2 x)
3.h(x) =cos(^12 x)+ 2
4.k(x) =−2 sin(^34 x)+ 1
5.j(x) =4 cos( 3 x)− 1
Graph each of the following functions.
6.f(x) =3 sin( 2 x)+ 1
7.g(x) = 2 .5 cos(πx)− 4
8.h(x) =−sin( 4 x)− 3
9.k(x) =^12 cos( 2 x)
10.j(x) =−2 sin(^34 x)− 1
Create an algebraic model for each of the following graphs.