Graph y=sin(x)-1

Problem

y=sin(x)−1

Solution

1. Identify the parent function, which is y=sin(x) This function has a period of 2*π an amplitude of 1 and oscillates between 1 and −1

2. Determine the transformation applied to the parent function. The expression sin(x)−1 indicates a vertical shift downward by 1 unit.

3. Find the new midline of the graph. The original midline y=0 shifts down to y=−1

4. Calculate key points for one period [0,2*π] by subtracting 1 from the standard yvalues of the sine function.

• At x=0 y=sin(0)−1=−1

• At x=π/2 y=sin(π/2)−1=0

• At x=π y=sin(π)−1=−1

• At x=(3*π)/2 y=sin((3*π)/2)−1=−2

• At x=2*π y=sin(2*π)−1=−1

5. Plot the points and draw a smooth wave through them. The graph will oscillate between a maximum of 0 and a minimum of −2

Final Answer

y=sin(x)−1

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