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How do you graph # y=sin(x-135)#?

Answer 1

Delilah Aguilar

As below.

Standard form of sine function is #y = A cos (Bx - C) + D#

#y = sin (x - 135^@) = sin (x - (3pi)/4)#

#A = 1, B = 1, C = 3pi)/4, D = 0#

#Amplitude = |A| = 1#

Period #= (2 pi)/ |B| = (2 pi)/ 1 = 2pi#

Phase shift # = -C / B = ((-3pi)/4) / 1 = -(3pi)/4#, #color(red)((3pi)/4)# to the LEFT.

Vertical Shift #= D = 0#

graph{sin (x-((3pi)/4)) [-10, 10, -5, 5]}

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Answer 2

Josiah Anderson

To graph the function ( y = \sin(x - 135^\circ) ), follow these steps:

Identify the amplitude of the sine function, which is 1.
Determine the period of the sine function, which is ( 2\pi ).
Find the phase shift by setting ( x - 135^\circ = 0 ) and solving for ( x ). In this case, ( x = 135^\circ ).
Plot the key points of the sine function, starting from ( x = 0 ) to ( x = 360^\circ ) (or ( 2\pi ) radians), considering the phase shift.
Connect the points smoothly to form the graph.

That's it.

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