(x) in the identity for cos(2x) and then
solve for cos
2
(x) in terms of what remains.
cos
2
(x) =
(d) Uniformly replace x by
θ
/2 in the identity for cos
2
(x)
that you obtained in part (c) above in order to obtain an
identity for cos
2
(
θ
/2).
Clean up the algebra.
cos
2
(
θ
/2) =
(e) Modify steps (c) and (d) appropriately to obtain a
corresponding identity for sin
2
(
θ
/2).
Show your work neatly.
sin
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View Full DocumentFinal Exam/MAC1114
Page 7 of 8
24. (10 pts.)
To measure the height of the top of a distant
object , a surveyor takes two sightings of the top of the object
5000 feet apart. The first sighting, which is nearest the object,
results in an angle of elevation of 45°.
The second sighting,
which is most distant from the object, results in an angle of
elevation of 30°.
If the transit used to make the sightings is 5
feet tall, what is the height of the object. You may assume the
object is on a level plane with the base of the transit.
25. (15 pts.)
Sketch the given curve in polar coordinates.
Do
this as follows: (a) Carefully sketch the auxiliary curve, a
rectangular graph on the coordinate system provided. (b) Then
translate this graph to the polar one.
Equation:
r=1+2 sin(
θ
)
(a)
r
θ
(b)
y
x
Final Exam/MAC1114
Page 8 of 8
26. (10 pts.)
Very carefully sketch the graph of the equation
(
x+1
)
2
= 4(y  2) below.
y
x
27. (5 pts.) Use the Law of Sines to solve the triangle with
α
= 115°,
γ
=3
0°
,a
n
dc=3
. Y
o
um
a
y assume that the standard
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 Spring '08
 Storfer
 Trigonometry, Tan, pts, Final Exam/MAC1114

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