Trig Graphing Study Sheet
Name____________________________
I. Graphing Sine and Cosine
A. In the graph of
f (θ ) = sin θ , the independent variable is ____________________ and
the dependent variable is _______________________. The independent variable is (almost) always measured in
______________________ and the dependent variable is measured in _______________.
B. Evaluate the following without using a calculator:
sin 0 =
sin π =
6
sin π =
4
sin π
=
sin
π =
sin
π
=
cos 0 =
cos π =
cos π =
4
cos π
=
cos
π =
cos
π
=
6
3
3
2
2
C. The five primary points/helpful graphing points for graphing sin θ are:
(
)(
)(
)(
)(
)
D. The five primary points/helpful graphing points for graphing cos θ are:
(
E. Over the interval (0,
F. Over the interval (0,
π
2
π
2
)(
)(
)(
)(
)
), the sine function is (increasing or decreasing)?
), the cosine function is (increasing or decreasing)?
G. What is the domain of the parent sine and cosine functions?
The range?
H. What is the amplitude of the parent sine and cosine functions?
The period?
Where does a “usual” cycle start and finish?
II. Transformations of Sine and Cosine
A. Given the general form f(x) = a sin b(x – h) + k , describe the graph of f(x) compared to the parent graph
g(x) = sin x, when:
1) a = 3
3) a = -1 and h =
2) b = π
−π
4
B. Compare the graph of y = sin 4(x –
similarities.
4) b = ½ and k = -2
π
2
) to the graph of y = sin (4x) –
π
2
. Use words to explain the differences and
C. Write an equation for the graph of
⎛ ⎛
π ⎞⎞
y = sin ⎜ 2 ⎜ x − ⎟ ⎟ using cosine: _______________________
4 ⎠⎠
⎝ ⎝
Using sine with a different phase shift: _______________________
D. Graph the following:
a) y = - sin 4(x –
π
8
)+1
b) y = 3cos
π
2
x–2
III. Applications of Sine and Cosine
A. The depth of water at a surfing spot in Honolulu, HI varies from 9 ft to 17 ft, depending on the
time. This Saturday high tide is scheduled to occur at 6:00 am and then again at 6:00 pm. Create
a model to describe the depth of water as a function of time t in hours since 8:00am on Saturday.
B. In a Canadian region the population of migratory geese can be modeled according to the
equation G = 3020 + 3000sin
π
t, where t = the time in months since April 15.
6
a) What is the highest the population reaches, and when does this occur?
b) When is the population of geese 3020 or less?
IV. Graphing Tangent and Cotangent
A. Evaluate the following without using a calculator:
tan 0 =
tan π =
6
tan π =
4
tan π
=
tan
π =
tan
π
=
cot 0 =
cot π =
cot π =
4
cot π
=
cot
π =
cot
π
=
6
3
3
2
2
B. What is the domain of y = tan x?
The range?
C. What is the domain of y = cot x?
The range?
D. Is the graph y = tan x increasing or decreasing?
y = cot x?
E. What is the period for y = tan x and y = cot x? Where does the “usual” cycle start and finish?
F. Write an equation using tangent that matches the graph of y = cot x.
G. Graph the following functions:
a) a) y = -2 tan x
b) a) y = cot x+3
V. Graphing Secant and Cosecant
A. Evaluate the following without using a calculator:
sec 0 =
sec π =
6
sec π =
4
sec π
=
sec
π =
sec
π
=
csc 0 =
csc π =
csc π =
4
csc π
=
csc
π =
csc
π
=
6
3
3
2
2
B. sin θ and csc θ are equal for what values in 0 ≤ θ ≤ 2π ?
C. cos θ and sec θ are equal for what values in 0 ≤ θ ≤ 2π ?
D. Graph the following functions:
a) y = csc (x) – 3
b) y = 2sec x
VI. Writing Equations for Trigonometric Graphs
A. Write a sine or cosine equation for the following graphs:
NOTE: Each unit marked on the x-axis is
π
2
. Each unit on the y-axis is one.
B. Write another function for each graph above using sine instead of cosine and vice versa.
¶ ¶ ¶ Now go back and review your quizzes and homework! ¶ ¶ ¶