Question

Which trigonometric function is equivalent to lower f left parenthesis x right parenthesis equals sine x?
(1 point)
Responses

lower f left parenthesis x right parenthesis equals cosine left parenthesis x minus start fraction 3 pi over 2 end fraction right parenthesis
Image with alt text: lower f left parenthesis x right parenthesis equals cosine left parenthesis x minus start fraction 3 pi over 2 end fraction right parenthesis

lower f left parenthesis x right parenthesis equals cosine left parenthesis x minus start fraction pi over 2 end fraction right parenthesis
Image with alt text: lower f left parenthesis x right parenthesis equals cosine left parenthesis x minus start fraction pi over 2 end fraction right parenthesis

lower f left parenthesis x right parenthesis equals cosine left parenthesis negative x minus start fraction pi over 2 end fraction right parenthesis
Image with alt text: lower f left parenthesis x right parenthesis equals cosine left parenthesis negative x minus start fraction pi over 2 end fraction right parenthesis

Answer 1

The function \( f(x) = \sin(x) \) can be expressed in terms of the cosine function using the phase shift identities. The sine function can be rewritten as:

\[
\sin(x) = \cos\left(x - \frac{\pi}{2}\right)
\]

Thus, the correct equivalent expression for \( f(x) = \sin(x) \) from the provided options is:

\[
f(x) = \cos\left(x - \frac{\pi}{2}\right)
\]

So, the answer is:

**lower f left parenthesis x right parenthesis equals cosine left parenthesis x minus start fraction pi over 2 end fraction right parenthesis**.