How do you sketch the graph of y = sin(x)?

To sketch the graph of \( y = \sin(x) \), plot key points and draw a smooth, continuous wave.

First, understand that the sine function is periodic, meaning it repeats its pattern every \( 2\pi \) radians (or 360 degrees). The basic shape of the sine wave starts at the origin (0,0), rises to a maximum of 1 at \( \pi/2 \) radians (90 degrees), returns to 0 at \( \pi \) radians (180 degrees), drops to a minimum of -1 at \( 3\pi/2 \) radians (270 degrees), and returns to 0 at \( 2\pi \) radians (360 degrees).

To sketch the graph, start by drawing the x-axis and y-axis. Mark the key points on the x-axis: 0, \( \pi/2 \), \( \pi \), \( 3\pi/2 \), and \( 2\pi \). On the y-axis, mark the points 1 and -1, which are the maximum and minimum values of the sine function.

Next, plot the key points: (0,0), \( (\pi/2, 1) \), \( (\pi, 0) \), \( (3\pi/2, -1) \), and \( (2\pi, 0) \). These points represent one complete cycle of the sine wave.

Now, draw a smooth, continuous curve through these points. The curve should start at the origin, rise to the maximum point at \( \pi/2 \), fall back to zero at \( \pi \), drop to the minimum point at \( 3\pi/2 \), and return to zero at \( 2\pi \).

Remember, the sine wave continues infinitely in both directions, so you can extend the pattern to the left and right if needed. The wave should be smooth and continuous, with no sharp corners or breaks.