Graph y=-sin(x)

Problem

y=−sin(x)

Solution

1. Identify the parent function and its key characteristics. The parent function is y=sin(x) which has a period of 2*π an amplitude of 1 and passes through the origin (0,0)

2. Determine the transformation applied to the parent function. The negative sign in front of the function, y=−sin(x) represents a reflection across the xaxis.

3. Calculate key points for one full period (0≤x≤2*π by negating the yvalues of the standard sine wave.

• 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. Plot the points and draw a smooth wave. The graph starts at the origin, goes down to a minimum of −1 returns to the xaxis, rises to a maximum of 1 and returns to the xaxis.

Final Answer

y=−sin(x)

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