Graph y=sin(x)

Problem

y=sin(x)

Solution

1. Identify the function as the basic sine function, which is a periodic trigonometric function with a period of 2*π and an amplitude of 1

2. Determine key points within one period from 0 to 2*π by evaluating the sine of standard angles.

3. Calculate coordinates for the intercepts, maximums, and minimums:

• At x=0 y=sin(0)=0

• At x=π/2 y=sin(π/2)=1

• At x=π y=sin(π)=0

• At x=(3*π)/2 y=sin((3*π)/2)=−1

• At x=2*π y=sin(2*π)=0

4. Sketch the curve by plotting these points (0,0) (π/2,1) (π,0) ((3*π)/2,−1) and (2*π,0) and connecting them with a smooth, continuous wave.

5. Extend the graph in both directions by repeating the pattern every 2*π units along the x-axis.

Final Answer

y=sin(x)

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