Write the sine

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

1 answer

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:

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