Precalculus Bc/ap Calculus Ab Summer Assignment Worksheet Page 4
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1
2
3
41 cos 2x
y
24) Consider the function
.
2
a) Can x take on any real value?
cos 2x
b) How large can
become? How small?
1 cos 2x
c) How large can
become? How small?
2
d) What are the domain and range of the original function?
25) Draw and label the sides and angles of the two special triangles, 30-60-90 and 45-45-90.
26) Use the following information to find the radian measure of the angle described by:
1
1
1
a)
revolution clockwise
b)
revolutions counterclockwise
8
3
3
1
1
2
c)
revolutions counterclockwise
d)
revolutions clockwise
4
2
27) Under the given conditions, find sin
or cos , whichever is not given, and state the quadrant
lies in.
3
1
a) cos =
, sin
> 0
b) sin =
, cos
< 0
5
2
12
5
c) sin =
, cos
> 0
d) cos =
, sin
> 0
5
13
Use special triangles and the unit circle to get the values for the following problems. SHOW ALL
WORK.
28) Simplify:
2
2
2
2
a) cos
cos
+ sin
cos
b) cos
sin
+ cos
sin
3
6
3
6
3
6
6
3
29) Evaluate:
1
1
arccos
arcsin
a) sin
b) cos
3
4
1
3
1
arcsin
cos
c) tan
d) sec
2
5
30) Arrange these in order from least to greatest:
3
1
1
3
a) arccos
, arcos 0, arccos
b) arctan
, arctan 0, arctan
2
2
2
31) Find the value of each:
1
3
1
3
sin arcsin
arccos
cos arcsin
arccos
a)
b)
2
2
2
2
1
cos 2arcsin
tan arctan 3
c)
d)
5
3
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