Grade 11 · Math · Algebra 2

11th grade Graph sine and cosine, and read amplitude, period, midline and phase shift worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Graph sine and cosine, and read amplitude, period, midline and phase shift

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Esme compares y = 2 sin(3x − π/4) + 1 with y = 2 sin(3x) + 1. Which way and how far are the rows moved?
- right π/12
- left π/12
- right π/4
- left π/4
2.
Jun compares y = cos(2x + π/3) − 2 with y = cos(2x) − 2. Which way and how far are the rows moved?
- right π/6
- left π/3
- right π/3
- left π/6
3.
Luz compares y = 4 cos(2x − π/2) + 1 with y = 4 cos(2x) + 1. Which way and how far are the rows moved?
- left π/4
- right π/2
- right π/4
- left π/2
x = π/4, 3π/4, 5π/4, 7π/4, 9π/4; y = 3, -1, -5, -1, 3. Noah made this table for one cycle of a shifted sine graph. What is the period, in terms of π?
x = π/2, 2π/3, 5π/6, π, 7π/6; y = 6, 4, 2, 4, 6. Pia made this table for one cycle of a shifted sine graph. What is the period, in terms of π?
x = π/3, 7π/12, 5π/6, 13π/12, 4π/3; y = -4, 0, 4, 0, -4. Ren made this table for one cycle of a shifted sine graph. What is the period, in terms of π?
Zee graphs y = -3 sin(2x − π/2) + 4. What is the greatest value of y?
Ari graphs y = 5 cos(3x + π) − 4. What is the least value of y?
Bo graphs y = -6 cos(x/2 + π/4) − 1. What is the greatest value of y?
Esme graphs y = 4 sin(3x − 3π/4) + 9. What is the least value of y?

11th grade Graph sine and cosine, and read amplitude, period, midline and phase shift worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Graph sine and cosine, and read amplitude, period, midline and phase shift. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can fill the key rows of a sine or cosine table and plot one cycle.
I can read the amplitude, period, midline and phase shift from an equation or a graph.
I can find the greatest and least values of a sine or cosine graph.

Standard: F-IF.C.7e, F-TF.B.5 (related)

Words to know

unit circle unrolled: The circle's heights laid out in a table, angle across, height up.

amplitude: How far the graph rises above its midline; never negative.

midline: The middle height, halfway between the highest and lowest rows.

period: How far across before the rows start repeating.

phase shift: How far the rows slide left or right.

key rows: The five rows of one cycle: start, quarter, half, three quarters, end.

Common mistakes

Your child used the whole distance from the lowest to the highest height.

Your child gave the highest height instead of the height above the middle line.

Your child gave the amplitude with a minus sign.

What to say

Ask: how far is the top above the middle line?

Ask: where is the middle line, and how far above it is the top?

Ask: can a height above the middle line be negative?

Questions parents ask

What is the most common mistake with graph sine and cosine, and read amplitude, period, midline and phase shift?

Your child used the whole distance from the lowest to the highest height.

How can I help my child with graph sine and cosine, and read amplitude, period, midline and phase shift?

Ask: how far is the top above the middle line?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

See all Algebra 2

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records