Question

Write the equation of the sinusoidal function shown.

A) y = cos x - 1
B)y=sin x - 1
C) y=2 sin x - 1
D) y = 2 cos x - 1

Answer 1

A. y= cos x - 1

Explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.

longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)

for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)