Graph y=sin(x-pi/4)

Problem

y=sin(x−π/4)

Solution

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

2. Determine the phase shift by looking at the argument of the sine function. The expression x−π/4 indicates a horizontal shift to the right by π/4 units.

3. Calculate key points for one full period by adding the phase shift π/4 to the standard xcoordinates of y=sin(x)

(x_1)=0+π/4=π/4

(x_2)=π/2+π/4=(3*π)/4

(x_3)=π+π/4=(5*π)/4

(x_4)=(3*π)/2+π/4=(7*π)/4

(x_5)=2*π+π/4=(9*π)/4

4. Map the y-values to these new xcoordinates. The yvalues remain 0, 1, 0, -1, 0$ respectively.

(π/4,0)

((3*π)/4,1)

((5*π)/4,0)

((7*π)/4,−1)

((9*π)/4,0)

5. Sketch the graph by plotting these points and drawing a smooth sinusoidal wave through them, extending the pattern in both directions.

Final Answer

y=sin(x−π/4)

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