Question

trig function given features (sin/cos) l1
2/3 penalty: none
write a cosine function that has a midline of ( y = 5 ), an amplitude of 3 and a period of ( \frac{pi}{4} ).
answer attempt 1 out of 5
( f(x)=)

Explanation:

Step1: Determine the general form of the cosine function

The general form of a cosine function is \(y = A\cos(Bx - C)+D\).

• The amplitude \(|A|\) is given. Here \(A = 3\) (since amplitude is \(3\)).
• The mid - line \(y = D\). Given \(D = 5\).
• The period formula is \(T=\frac{2\pi}{|B|}\). Given \(T=\frac{\pi}{4}\), then \(\frac{\pi}{4}=\frac{2\pi}{|B|}\). Solving for \(B\):

$$
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We can take \(B = 8\) (since there is no phase - shift information, \(C = 0\)).

Step2: Write the function

Substitute \(A = 3\), \(B = 8\), \(C = 0\), and \(D = 5\) into the general form \(y = A\cos(Bx - C)+D\). The function is \(y=3\cos(8x)+5\)

Answer:

\(f(x)=3\cos(8x)+5\)