Question

what is the maximum of f(x) = sin(x)?
-2π
-1
1
2π

Explanation:

Step1: Recall sine function range

The sine function \( f(x)=\sin(x) \) has a range of \( [-1, 1] \), meaning \( -1 \leq \sin(x) \leq 1 \) for all real \( x \).

Step2: Identify maximum value

From the range, the maximum value within \( [-1, 1] \) is \( 1 \). The other options (\( -2\pi \), \( -1 \), \( 2\pi \)) do not represent the maximum of \( \sin(x) \) ( \( -2\pi \) and \( 2\pi \) are outside the range of sine, and \( -1 \) is the minimum).

Answer:

C. 1