To rewrite the sine function \( f(x) = -2\sin(4x - \pi) + 3 \) as a cosine function, we can use the identity that relates sine and cosine:
\[ \sin(\theta) = \cos\left(\theta - \frac{\pi}{2}\right) \]
In our case, let \( \theta = 4x - \pi \). We can rewrite \( \sin(4x - \pi) \) as:
\[ \sin(4x - \pi) = \cos\left((4x - \pi) - \frac{\pi}{2}\right) = \cos\left(4x - \frac{3\pi}{2}\right) \]
Now we can substitute this expression back into our function:
\[ f(x) = -2\sin(4x - \pi) + 3 \] \[ = -2\cos\left(4x - \frac{3\pi}{2}\right) + 3 \]
Combining the constant outside the cosine gives us:
\[ f(x) = 3 - 2\cos\left(4x - \frac{3\pi}{2}\right) \]
Thus, the sine function \( f(x) = -2\sin(4x - \pi) + 3 \) can be rewritten as:
\[ f(x) = 3 - 2\cos\left(4x - \frac{3\pi}{2}\right) \]
1 answer