Trigonometry I
Copyright © 2006, Barry Mabillard.
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1.
The minimum and the maximum of a trigonometric function are shown in the diagram.
a)
Write a cosine equation for the function
Trigonometry I Standards Test Practice Exam - ANSWERS
1
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First determine the parameters a, b, c, & d.
(
)
7 - -3
max-min
10
a=
=
=
= 5
2
2
2
*The horizontal distance between
the two points is 8 units, so a full
cycle (the period) is 16 units.
π
π
π
2
2
b=
=
=
P
16
8
c = 5
(
that is where the cosine pattern begins
)
min+max
-3+7
4
d =
=
=
= 2
2
2
2
The equation is
(
)
⎡
⎤
⎢
⎥
⎣
⎦
y=5cos
x-5
+2
8
π
b)
Determine the value of the
y
– intercept, correct to three decimal places
Find the y-intercept by setting x = 0, then solving for y.
(
)
(
)
π
π
π
⎡
⎤
⎢
⎥
⎣
⎦
⎡
⎤
⎢
⎥
⎣
⎦
⎡
⎤
⎢
⎥
⎣
⎦
y = 5cos
x-5
+2
8
y = 5cos
0-5
+2
8
-5
y = 5cos
+2
8
y=0.087
Alternatively, graph in your
calculator and type
2
nd
→
Trace
→
Value
→
x
= 0
2.
Convert
11
18
π
to degrees
π
π
o
11
180
×
=
18
o
110