How do you sketch #y = 2 cos 3 (x - (pi/4))#?

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Answer 1 · 2018-06-07T06:35:22

As below.

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

Given #y = 2 cos 3(x - pi/4) = 2 cos (3x - (3pi)/4)#

#Amplitude = |A| = 2#

#"Period " = (2pi) / |B| = (2pi) / 3#

#"Phase Shift " = -C / B = ((3pi)/4) / 3 = pi/4#, #color(red)(pi/4# to the right

#"Vertical Shift " = D = 0#

graph{2 cos (3x - (3pi)/4) [-10, 10, -5, 5]}