Question

function f(x) = -2sin(x-pi)+3 as a cosine function. In 2 sentences explain how you got your answer

Answer 1

To rewrite the function \( f(x) = -2\sin(x - \pi) + 3 \) as a cosine function, I used the identity \( \sin(x) = \cos\left(x - \frac{\pi}{2}\right) \). This transforms the sine function into a cosine function, yielding \( f(x) = -2\cos\left(x - \pi - \frac{\pi}{2}\right) + 3 \), or more simply \( f(x) = -2\cos\left(x - \frac{3\pi}{2}\right) + 3 \).