Rewrite the sine function f(x)=−2sin(x−π)+3 as a cosine function. In 1–2 sentences, explain how you arrived at your answer.(2 points)

Answer 1

To rewrite the sine function \( f(x) = -2\sin(x - \pi) + 3 \) as a cosine function, we can use the identity \( \sin(x) = \cos(x - \frac{\pi}{2}) \). Thus, we rewrite it as \( f(x) = -2\cos\left((x - \pi) - \frac{\pi}{2}\right) + 3 \), which simplifies to \( f(x) = -2\cos(x - \frac{3\pi}{2}) + 3 \). This shows the sine function expressed in terms of a cosine function, with an adjusted phase shift.