How do you find the critical points to graph #y=3sin(1/3x+ pi/2)-2#?

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Answer 1 · 2018-05-05T02:58:49

As below.

#y = A sin (Bx - C) + D#

#color(brown)(Amplitude = |A|, " Period " = (2pi) / |B|, " Phase Shift " = -C / B, " Vertical Shift " = D#

#"Given Equation is " y = sin ((1/3)x + (pi/2)) -2#

#Amplitude = |A| = 3#

#"Period " = (2pi) / |B| = (2pi) / (1/3) = 6pi#

#"Phase Shift " = -C / B = -(pi/2) / (1/3) = - (3pi)/2, color(crimson)((3pi)/2 " to the LEFT"#

#"Vertical Shift " = D = -2, color(crimson)(" 2 down"##

graph{3 sin ((1/3)x + (pi/2)) - 2 [-10, 10, -5, 5]}