38.4k views
4 votes
Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function

shown below:
·10 -18 -17 -16 -15 -14 -14 -12 -11 -10
y =
#
7
6
Question Help: Video
Submit Question
$

9
2
+
-2
Leave your answer in exact form; if necessary, type pi for .
-6

Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches-example-1

1 Answer

6 votes

The trigonometric function matching the graph with an amplitude of 9, midline at 2, and a period of π is y = 9 sin(2x) + 2, using the sine function form y = A sin(kx) + C.

Given:

Amplitude
(\(A\)) =
\(9\)

Midline
(\(C\)) =
\(2\)

Period =
\(\pi\)

For a sine function
\(y = A \sin(kx) + C\):


\(A = 9\)(Amplitude)


\(C = 2\) (Midline)

Period =
\(\pi\)

The general formula for the sine function is
\(y = A \sin(kx) + C\).

The formula for a sine function with amplitude
\(A\) , period
\(P\) , and midline
\(C\) is:


\[y = A \sin\left((2\pi)/(P)x\right) + C\]

Using the given values:


\[y = 9 \sin\left((2\pi)/(\pi)x\right) + 2\]

Simplify:


\[y = 9 \sin(2x) + 2\]

Therefore, the trigonometric function that matches the graph is
\(y = 9 \sin(2x) + 2\).

Certainly! Here's a question based on the provided information:

Question:

Find a trigonometric function of the form
\(y = A \sin(kx) + C\) or \(y = A \cos(kx) + C\) that fits the graph provided. The function should have an amplitude of
\(9\),a midline of
\(2\) , and a period of
\(\pi\). Provide the function in exact form, using "pi" for \(\pi\).

User Spinlok
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories