The graph of f(x) = sin(x+c) is shifted π/4 units to the right when compared to the graph of g(x) = sinx . What is the value of c?(1 point) Responses −π4 negative pi over 4 π4 pi over 4 1 1 -1
The graph of \(f(x) = \sin(x+c)\) is shifted \(\frac{\pi}{4}\) units to the right when compared to the graph of \(g(x) = \sin(x)\).
This means that the graph of \(f(x)\) intersects the x-axis at \(\pi/4\), while the graph of \(g(x)\) intersects the x-axis at 0.
Since the sine function has a period of \(2\pi\), we know that \(\sin(\pi/4 + c) = 0\) and \(\sin(0) = 0\).
This implies that \(\pi/4 + c = 0\), since both angles must yield the same result for the sine function.
Solving for \(c\), we have \(c = -\pi/4\).
Therefore, the value of \(c\) is \(\boxed{-\pi/4}\).