need help with trigonometry
Brian_1234
hmd.doc1)
÷
ø
ö
ç
è
æ
=
3
2
,
5
)
,
(
p
q
r
Find the unknown sides and angles of these triangles:
2) You happen to know the radio tower on the top of a building is 30 feet tall. To find how far you are from the building, you measure the angle of elevation to the bottom of the tower to be 20 degrees, and the angle of elevation to the top of the tower to be 23 degrees. How far from the building are you.
3) Convert the polar coordinate
4) Convert the Cartesian coordinate
)
7
,
4
(
)
,
(
-
-
=
y
x
to a polar coordinate5) Rewrite the equation
9
2
2
=
+
y
x
as a polar equation6) Rewrite the equation
2
=
x
as a polar equation7) Rewrite the equation
)
sin(
2
q
=
r
as a Cartesian equation8) Rewrite the equation
)
2
sin(
q
=
r
as a Cartesian equation (hint: use an identity)9) Sketch a graph of
)
3
sin(
q
=
r
. For what values of θ is the graph at the origin? The furthest from the origin?10) Multiply:
(34)(2)
ii
+-
11) Divide:
32
4
i
i
-
+
12) Rewrite in polar form:
512
i
+
13) Rewrite in Cartesian form:
6
7
i
e
p
14) Calculate
4
512
i
+
. Give your answer in a+bi form.15) Given the vectors shown, sketch
34
uv
-
rr
16) A man walks 5 miles north, 3 miles at 30o north of east, 4 miles southeast, and 2 miles west.
a. Draw a picture showing the man’s path as set of vectors
b. Resolve each vector into components
c. Find the vector showing the man’s total displacement (the vector from where he started to where he ended up)
d. How far is the man from where he started at the end of his walk?
e. In what direction should he walk to get back to his starting position?
17) Parameterize the curve:
2
3
xy
=-
18) Rewrite as a Cartesian equation:
3
1
sin()
xt
ytt
ì
=+
í
=-
î
19) Rewrite as a Cartesian equation:
2cos()
3sin()
xt
yt
=
ì
í
=
î
20) Find a possible equation of the form
sin()
cos()
xat
ybt
=
ì
í
=
î
for:
6
5
3
130o
12
20o
