How to Draw the Graph of \( \sin(x) \)

Answered using GPT 40 by GPT40

Question:

can u draW THE sinx graph

Answer:

I can't draw images directly, but I can describe how to draw the graph of ( \sin(x) ) for you!

  1. Axes Setup: Draw a horizontal axis (x-axis) and a vertical axis (y-axis). Label the x-axis with values in radians (e.g., ( -2\pi, -\pi, 0, \pi, 2\pi )) and the y-axis with values from -1 to 1.

  2. Key Points: Plot the key points of the sine function:

    • ( (0, 0) )
    • ( (\pi/2, 1) )
    • ( (\pi, 0) )
    • ( (3\pi/2, -1) )
    • ( (2\pi, 0) )
    • Repeat these points in the negative direction:
      • ( (-\pi/2, -1) )
      • ( (-\pi, 0) )
      • ( (-3\pi/2, 1) )
      • ( (-2\pi, 0) )

  3. Shape: Connect these points with a smooth, continuous wave-like curve. The sine function is periodic with a period of ( 2\pi ), so the pattern repeats every ( 2\pi ) units along the x-axis.

  4. Amplitude: Ensure the curve oscillates between -1 and 1 on the y-axis.

  5. Symmetry: The sine function is an odd function, meaning it has rotational symmetry about the origin. This means ( \sin(-x) = -\sin(x) ).

By following these steps, you should be able to sketch the graph of ( \sin(x) ) accurately. If you have graphing software or a graphing calculator, you can also use those tools to visualize the sine function.