Graph y=sin(x-pi)

Problem

y=sin(x−π)

Solution

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

2. Determine the phase shift by looking at the horizontal translation inside the sine function. The form y=sin(x−c) indicates a shift of c units to the right.

3. Calculate the shift value, which is π This means every point on the standard sine wave is shifted π units to the right.

4. Plot the key points for one period. The starting point (0,0) moves to (π,0) The peak (π/2,1) moves to ((3*π)/2,1) The midpoint (π,0) moves to (2*π,0) The trough ((3*π)/2,−1) moves to ((5*π)/2,−1) The end point (2*π,0) moves to (3*π,0)

5. Sketch the smooth periodic wave through these points. Note that because sin(x−π)=−sin(x) the graph is also a reflection of the standard sine wave across the x-axis.

Final Answer

y=sin(x−π)

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