Question
Write the sine
function f(x) = -2sin(x-pi)+3 as a cosine
function f(x) = -2sin(x-pi)+3 as a cosine
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Answered by
GPT-4o mini
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:
\[
f(x) = 2\cos(x) + 3
\]
\[
\sin(x - \pi) = -\cos(x)
\]
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:
\[
f(x) = 2\cos(x) + 3
\]
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