Question

graph exactly one cycle of the function f(x) = sin(7x). identify the maximum, minimum, and period of the function maximum: minimum: period: you must answer all questions above in order to submit.

Explanation:

Step1: Recall sine function properties

The general form of a sine function is \( f(x) = A\sin(Bx + C) + D \). For \( f(x)=\sin(7x) \), \( A = 1 \), \( B = 7 \), \( C = 0 \), \( D = 0 \).

Step2: Find maximum value

The range of \( \sin(\theta) \) is \( [-1, 1] \). Since \( A = 1 \) and \( D = 0 \), the maximum value of \( \sin(7x) \) is \( 1 \).

Step3: Find minimum value

Using the range of sine function, the minimum value of \( \sin(7x) \) is \( -1 \).

Step4: Find period

The period of \( \sin(Bx) \) is \( \frac{2\pi}{|B|} \). Here, \( B = 7 \), so period is \( \frac{2\pi}{7} \).

Answer:

Maximum: \( 1 \)
Minimum: \( -1 \)
Period: \( \frac{2\pi}{7} \)