Day 2 Homework (Answers):
1. State the phase shift for each trigonometric function.
a) y = sin (x - 60˚) 60˚ right
b) y = cos (x + 90˚)
c) y = sin (x + 30˚) 30˚ left
d) y = cos (x - 45˚)
90˚ left
45˚ right
2. Determine the vertical shift and state the range of each function.
a) y = sinx + 3
up 3
b) y = cosx – 4
c) y = sinx – 6
down 6
d) y = cosx + 5
down 4
up 5
3. Determine the phase shift and the vertical shift with respect to y = sinx for each function.
a) y = sin(x + 46˚) + 2
left 46˚, up 2
b) y = sin(x - 65˚) – 5
right 65˚, down 5
4. Determine the phase shift and the vertical shift with respect to y = cosx for each function.
a) y = cos(x - 73˚) + 4
right 46˚, up 2
b) y = cos(x + 60˚) – 3
leftt 60˚, down 3
5. Determine the phase shift and/or vertical shift and graph one cycle of the function.
a) y = sinx + 1
no phase shift, up 1 b) y = cos(x + 30˚) left 30˚, no vertical shift
c) y = sin(x - 60˚) + 2 right 60˚, up 2
d) y = cos(x - 120˚) – 1 right 120˚, down 1
e) y = sin(x + 45˚) + 3 left 45˚, up 3
f) y = cos(x + 90˚) – 2 left 90˚, down 2
6. How can you tell from the equation of a sinusoidal function (sine or cosine) if a translation
represents a phase shift or a vertical shift?
A vertical shift is outside of the sinx or cosine x, such as y = sinx + 2 or y = cosx – 1.
A phase shift is inside brackets with the x, such as y = sin(x - 30˚) or y = cos(x + 45˚).
7. Write the equation of each transformed function.
a) The function y = sinx is transformed so that is has a phase shift left 58˚ and a vertical shift
down 4. y = sin(x + 58˚) - 4
b) The function y = cosx is transformed so that is has a phase shift right 67˚ and a vertical shift
up 5.
y = cos(x - 67˚) + 5
c) The function y = cosx is translated 41˚ left and 8 units down. y = cos(x + 41˚) - 8
d) The function y = sinx is translated 15˚ right and 2 units up.
y = sin(x - 15˚) + 2
8. For each graph, determine two equations, one in the form y = cos(x – d) + c and the other in the
form y = sin(x – d) + c.
y = sin(x - 60˚)
y = cos(x - 150˚)
y = sin(x + 30˚) + 1
y = cos(x - 60˚) + 1
y = sin(x - 45˚) - 2
y = cos(x - 135˚) - 2