ATHS FC – Math Department Al Ain
Assignment 1 (Term I)-Grade 11 Regular
Section
Date
Name
Lesson
ID
Marks
12.7 Graphing Trigonometric Functions
12.8 Translations of Trigonometric Graph
/5
Q1) Find the amplitude (or asymptotes) and period of each function. Then graph the function.
1
a) 𝑦 = 5𝐶𝑜𝑠 2 𝜃
Amplitude: 5,
Period:
360
1/2
=720
Draw dashed lines for
the amplitudes
b) 𝑦 = 3𝑡𝑎𝑛2𝜃
Asymptotes: ±45, ±135, ±225 …,
Period:
180
2
=90
ATHS-ALAin, FC/Math Grade 11 Regular
Page 1
Q2) State the amplitude, period, phase shift, and vertical shift for each function. Then graph the
function.
𝜋
a) 𝑦 = −3 + 2𝑆𝑖𝑛2(𝜃 + 4 )
Amplitude: 2,
Period:
360
2
=180
Phase shift:
𝜋
4
𝑡𝑜 𝑙𝑒𝑓𝑡
Vertical shift: 3 units to down
Draw dashed lines for the midline 𝑦 = −3 , and for the amplitude
b) 𝑦 = 4 + 3𝐶𝑜𝑠2𝑥
0 ≤ 𝑥 ≤ 2𝜋
360
Amplitude:3,
Period:
Phase shift:NO
Vertical shift: 4 units up
2
=180
Draw dashed lines for the midline 𝑦 = 4 , and
for the amplitude
You need to draw two cycles in this case
ATHS-ALAin, FC/Math Grade 11 Regular
Page 2
𝜋
Q3) WEATHER The function 𝑦 = 60 + 25𝑆𝑖𝑛 6 𝑡,where t is in months and t=0 corresponds to April
15, models the average high temperature in degrees Fahrenheit in Centerville.
a.
Determine the period of this function. What does this period represent?
2𝜋
Period: 𝜋/6 =12, every 12 months the weather will repeat itself.
b.
What is the maximum high temperature and when does this occur?
85 Fahrenheit, July 15
Q4) Write a trigonometric function that has amplitude of 5 and period of 720. Then graph the
function.
1
1
𝑦 = 5𝑠𝑖𝑛 2 𝜃 or 𝑦 = 5𝑐𝑜𝑠 2 𝜃
Q5) Match the function with its graph. 1-F 2-B 3-E 4- A 5-C 6-D
ATHS-ALAin, FC/Math Grade 11 Regular
Page 3