Lesson 26—Quiz 6 (40 points)
1. Convert each of the following angles from degrees to radians. (1 pt. each)
a) 45°
b) 135°
c) 270°
2. Convert each of the following angles from radians to degrees. (1 pt. each)
a)
2
p
b)
2
p
–
c)
4
5p
3. Find the length of an arc with angle
4
3p in a circle of radius 2. (1 pt.)
4. Without using a calculator, find sint for each of the following angles. (1 pt. each)
a)
6
p
b)
4
p
c) 0
d)
3
p
e)
2
p
f)
4
3p
g) p
h)
6
11p
5. Without using a calculator, find cos t for each of the following angles. (1 pt. each)
a) 0
b)
6
p
c)
4
p
d)
3
p
e)
2
p
f) p
g)
4
3p
h)
4
5p
i)
3
4p
6. Find all values of t in [0, 2p ] which satisfy the given equation. (1 pt. each)
a)
2
sin t = 2
b)
2
cos t = 1
c) cos t = -1
d)
2
sin t = – 1
e) sint = 0
f)
2
cos t = – 3
7. Use the graphs of the sine and cosine functions to sketch one period of the graph
of each of the following functions. (2 pts. each)
a) f (x) = 1+ cos x
b) )
2
( ) 2sin(
p
f x = x +
c) )
2
g(x) 1 cos( x p
= –
d) )
3
( ) 3sin(
+p
h x = x
8. Find a function of the form f (x) = A + BsinCx to approximate the following
data. (2 pts.)
x 0.5 1 1.5 2 2.5 3 3.5 4
y 0.71 1 0.71 0 -0.71 -1 -0.71 0
Lesson 30—Quiz 7 (31 points)
1. Given that cost
2
= 1 and
2
0
p
= t = , find each of the following. (1 pt. each)
a. sint
b. csct
c. cot t
2. Given that
3
sin t = – 2 and p
p
2
2
3 = t = , find each of the following. (1 pt. each)
a. sect
b. tan t
c. cost
3. Sketch one period of each of the following. (3 pts. each)
a. )
2
( ) 2sec(
p
f x = x – .
b. f (x) = tan x +1
4. Find all the values of t in [0, 2p ] such that | sec t | = 1 . (2 pts.)
5. Find the exact value of each of the following. (1 pt. each)
a. )
4
sec(
-p
b. )
12
cos(7
p
c. )
6
tan(7
p
d. )
3
csc(4
p
6. Find all the values of x in [0, 2p ] that satisfy (cos x)2 – 3sin x – 3 = 0 . (2 pts.)
7. A right triangle has one of its acute angles labeled ? . The opposite side has length
1, and the hypotenuse has length 2. Find the values of the six trigonometric
functions for the angle ? . (1 pt. each)
8. Suppose a right triangle has an acute angle of
6
p and a hypotenuse of length 4.
Find the lengths of the other two sides of the triangle. (2 pts.)
9. Near sunset, a 3-meter-tall pole casts a 3 3 -meter-long shadow. What is the
angle of elevation of the sun above the horizon at this time? (3 pts.)
Lesson 33—Quiz 8 (17 points)
1. Find the exact value of each of the following: (1 pt. each)
a) )
2
arcsin (1
b) arcsec (2)
c) arctan (1)
d) arccos (-1)
e) ))
8
tan (arcsin(3
f) ))
2
tan (arccos(- 1
g) ))
4
arcsec (sec(
p
h) ))
8
sin (arccos(7
2. Find all the solutions to the equation which lie in the
interval [-2
(cos x)2 + cos x – 2 = 0
p , 2p ]. (2 pts.)
3. Two cars leave a certain town at the same time. One travels north on a road at 30
mph, and the other travels northeast on a road at 25 mph. How far apart are the
two cars one hour after they departed? (3 pts.)
4. A ship is sailing west toward shore, and there are two ports on the horizon. The
ports are 17 miles apart, and from the ship’s vantage point, port A is north of
straight ahead and port B is south of straight ahead. Approximately how
much farther is it for the ship to dock at port B than at port A? (4 pts.)
30°
80°
Lesson 38—Quiz 9 (33 points)
1. Sketch the graph of each of the following functions. (2 pts. each)
a) f (x) = ex+2
b) g(x) = 2ln(x +1)
c) )
2
h(x) = -ln(1 x
d) f (x) =1- ex
2. Without using a calculator, evaluate each of the following. (1 pt. each)
a) ln1
b) eln e
c) )
3
log (1 3
d) e2 ln 6
e) log (128) 2
3. Rewrite ln x – 3ln(x +1) using a single logarithm. (1 pt.)
4. Solve each of the following for x. (2 pts. each)
a) ex+2 = 4
b) 0 = ln(x2 -3)
c) 4x = 2x+1
d) log 0 2 x x – x =
5. Suppose $1300 is invested in an account that earns 2% interest. For each of the
following compounding periods, determine the account’s value at the end of 2
years. (1 pt. each)
a) Annually
b) Monthly
c) Continuously
6. An investment of $500 is placed in an account earning 5% interest compounded
continuously. At what time after the deposit will this account have a value of
$1000? (2 pts.)
7. A bacterial colony initially contains 600 bacteria. One hour later it contains 610
bacteria. Assuming the colony grows exponentially, how may bacteria will there
be in the colony after 7 hours? (2 pts.)
8. Same situation as in question #7, except assume the colony grows linearly. (2 pts.)
9. A bacterial colony initially contains 100 bacteria. If it takes 4 hours for the
colony’s size to double, how long will it take for the colony’s size to triple,
assuming it grows exponentially? (2 pts.)
Lesson 44—Quiz 10 (45 points)
1. Sketch the graphs of each of the following conic sections. Label all relevant
features such as vertices, foci, etc. (3 pts. each)
a) y = -2×2
b) x2 + 2x + 4y2 – 3 = 0
c) x2 – 9y2 + 54y – 90 = 0
d) x + y2 +1 = 0
2. Find the equation for and sketch the parabola that has its focus at (1, 0) and that
has a directrix that passes through the point (-3, 0). (3 pts.)
3. Find the equation for and sketch the ellipse that has vertices at (-1, 0) and (5, 0)
and has y-intercepts of ±1 . (3 pts.)
4. Find the equation for and sketch the hyperbola that has vertices at (0, 0) and (0, 3)
and that passes through (1, -1). (3 pts.)
5. The following are points given in polar coordinates. Plot and convert each to
rectangular coordinates. (2 pts. each)
a) )
4
(1, 3
p
b) )
4
(-1, 3
p
c) )
6
(2, –
p
6. The following are points given in rectangular coordinates. Plot and convert each
to polar coordinates. (2 pts. each)
a) (0,-3)
b) (1, 0)
c) (- 3 , 1)
7. Sketch and label a graph of each of the following polar equations. (2 pts. each)
a) r =1
b)
4
7
p
? =
c) r = 2sin?
d) r = 3?
8. Let x(t) = 1+ 2sin t and y(t) = -2 + 3cos t be the parametric equations for some
graph.
a) Find a rectangular equation for this graph. (1 pt.)
b) Sketch and label the graph. (1 pt.)
9. Find a set of parametric equations for the line which passes through the points (-2,
1) and (7, 0). (2 pts.)