Question
Rewrite the sine fun gion f(x) = 2sin(x+pi/2) -1 as a cosine
Answers
GPT-4o mini
To rewrite the function \( f(x) = 2\sin\left(x + \frac{\pi}{2}\right) - 1 \) as a cosine function, we can use the sine to cosine relationship. Recall that:
\[
\sin\left(x + \frac{\pi}{2}\right) = \cos(x)
\]
Substituting this into the function, we have:
\[
f(x) = 2\cos(x) - 1
\]
Thus, the rewritten form of the function as a cosine is:
\[
f(x) = 2\cos(x) - 1
\]
\[
\sin\left(x + \frac{\pi}{2}\right) = \cos(x)
\]
Substituting this into the function, we have:
\[
f(x) = 2\cos(x) - 1
\]
Thus, the rewritten form of the function as a cosine is:
\[
f(x) = 2\cos(x) - 1
\]