Question

Write the sine
function f(x) = -2sin(x-pi)+3 as a cosine

Answer 1

To express the function \( f(x) = -2\sin(x - \pi) + 3 \) as a cosine function, we can use the relationship between sine and cosine. The sine function can be expressed in terms of cosine like this:

\[
\sin(x - \pi) = -\cos(x)
\]

Now, substitute this into the function:

\[
f(x) = -2\sin(x - \pi) + 3 = -2(-\cos(x)) + 3
\]

This simplifies to:

\[
f(x) = 2\cos(x) + 3
\]

Therefore, the function \( f(x) = -2\sin(x - \pi) + 3 \) can be rewritten as:

\[
f(x) = 2\cos(x) + 3
\]