Graph sin(x)^2

Problem

sin(x)

Solution

1. Identify the function as ƒ(x)=sin(x) which is a periodic function that oscillates between 0 and 1 because the square of any real number is non-negative and |sin(x)|≤1

2. Apply the identity for power reduction to rewrite the function in terms of a single trigonometric ratio:

sin(x)=(1−cos(2*x))/2

3. Determine the properties of the graph: the amplitude is 0.5 the vertical shift (midline) is y=0.5 and the period is (2*π)/2=π

4. Find key points within one period [0,π]

• At x=0 y=sin(0)=0

• At x=π/4 y=sin(π/4)=0.5

• At x=π/2 y=sin(π/2)=1

• At x=(3*π)/4 y=sin((3*π)/4)=0.5

• At x=π y=sin(π)=0

5. Sketch the curve by plotting these points and drawing a smooth, wave-like shape that repeats every π units along the x-axis.

Final Answer

sin(x)=1/2−1/2*cos(2*x)

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