Given the graphs of $y=\sin \left(x\right)$ and $y=\cos \left(x\right)$, which of the following points lies on the y-axis and is also on the line that passes through the point $(0,1)$ and is parallel to the line passing through points $(0,0)$ and $(\pi ,0)$?

• A. $(0,0)$
• B. $(0,1)$
• C. $(0,-1)$
• D. $(0,\pi )$

Answer: (B)

Verified step by step guidance

1. Identify the line passing through points (0, 0) and (\pi, 0). Since both points have y = 0, this line is horizontal with slope 0.
2. Since the required line is parallel to the line through (0, 0) and (\pi, 0), it must also be horizontal and have slope 0.
3. The line passes through the point (0, 1), so its equation is y = 1 (a horizontal line at y = 1).
4. Points that lie on the y-axis have x = 0. Substitute x = 0 into the line equation y = 1 to find the y-coordinate of the point on the y-axis: y = 1.
5. Therefore, the point on the y-axis and on the line parallel to the given line passing through (0, 1) is (0, 1).