How do you determine the amplitude, period, and shifts to graph #y = - sin 1/2 ( x + pi/2) - 1#?

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Answer 1 · 2018-07-04T01:55:28

As below.

Sine function format is #y = A sin( Bx - C) + D#

#y = - sin (x/2 + pi/4) - 1#

#A = -1, B = 1/2, C = -pi/4, D = -1#

#Amplitude = |A| = 1#

#"Period " = (2pi) / |B| = (2pi)/(1/2) = 4pi#

#"Phase Shift " = -C / B = (pi/4)/(1/2) = pi/2, color(crimson)(pi/2" to the RIGHT"#

#"Vertical Shift " = D = -1#

graph{- sin((1/2)x + pi/4) - 1 [-10, 10, -5, 5]}