What is the graph of $y = sin (x - \frac{π}{4})$ $y=sin(x-pi/4)$ ?

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Answer 1 · 2014-10-06T04:19:09

Remember back to the unit circle. The $y$ $y$ values correspond to sine.

$0$ $0$ radians $\to (1, 0)$ $-> (1,0)$ the result 0

$\frac{π}{2}$ $pi/2$ radians $\to (0, 1)$ $-> (0,1)$ the result is 1

$π$ $pi$ radians $\to (- 1, 0)$ $-> (-1,0)$ the result is 0

$\frac{3 π}{2}$ $(3pi)/2$ radians $\to (0, - 1)$ $-> (0,-1)$ the result is -1

$2 π$ $2pi$ radians $\to (1, 0)$ $-> (1,0)$ the result is 0

Each of these values are moved to the right $\frac{π}{4}$ $pi/4$ units.

Enter the sine functions.
The blue function is without the translation.
The red function is with the translation.

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Set the ZOOM to option 7 for Trig functions.

Press WINDOW and set the Xmax to $2 π$ $2pi$ the calculator converts the value to the decimal equivalent.

Set the Xmin to 0.

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Press the GRAPH button.

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What is the graph of y=sin(x−π4)y=sin(x-pi/4)?