Question

Find a function of the form

y
=
A
sin
(
k
x
)
+
C
or

y
=
A
cos
(
k
x
)
+
C
whose graph matches this one:
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
(Leave your answer in exact form; if necessary, type pi for
π
.
y
=

Answer 1

Answer:

Step-by-step explanation:

The amplitude is 6, so A=6.

Also, the midline is y=-3, so C=-3.

The period is 10, so 2pi/k = 10 -> k=5.

Now we need to determine if this is a sine graph or a cosine graph. As the y-intercept is not the value of C, we can determine that this is a cosine graph, and thus y=6cos(5x)-3.