Math 140
Hw 5
Recommended problems, don't turn this in.
A. Describe the combination of translations and/or
reflections needed to get the given function from f (x).
(a)
right 1
y fx 1
(b)
down 1
y fx 1
(c)
up 1
y fx 1
(d)
left 1
y fx 1
(e)
y-axis reflectio
Math 140
Hw 19
Recommended problems, don't turn this in.
Find the period and amplitude.
A.
period=
amplitude=
F. y 3 sin (x/2
amplitude=
6
period=
5
1
x-intercepts:
3 4
2
-6
increases on:
B.
period=
amplitude=
6
G. y cos 2x
4
amplitude=
2
-2
2
4
period=
x
Math 140
Hw 18
Recommended problems, don't turn this in.
For A-D: (a) Rewrite in terms of an angle in [0,p/2]. (b) Find the
exact answer, no decimals. See the example. point each.
sec 2 tan 2
1cot 2
F. Simplify:
A(a). cos11/6
A(b). cos11/6
G. Prove: csc
Math 140
Hw 17
Recommended problems, don't turn this in.
Simplify.
sin 2 Acos 2 A
A. sin Acos A
q
Hint: factor the top.
3
B. sin 2 cos csc 3 sec
4x
b
C. cot B sin 2 B cot B
D.
3
2x
cos 2 Acos A12
N. Find sin q, cos q, tan q.
cos A3
tan
tan
E. sec 1 sec
Math 140
Hw 16
For each angle, sketch the reference angle, draw an
arrow to indicate the angle's direction. A reference
angle must be positive and < /2 = 90o.
A. (a) 110o
(b) 60o
Recommended problems.
sin cos
F. Simplify cos sin .
G. Factor tan 2 + 8 tan
Math 140
Hw 25 Recommended problems, dont turn this in.
2sina has 5 symbols, 2sin(a) has 7 symbols.
A. When earth E, Mercury M, and the sun S are lined up
so that VEMS is a right angle, VSEM is 21o. Given that
the distance ES from the earth to the sun is
Math 140
Hw 24 Recommended problems, dont turn this in.
Evaluate exactly without a calculator: p and 2 rather than
3.14 or 1.41. Answer may be undef.
L. sintan 1 1
5 symbol fraction with square root
A. sin 1 3 /2
1
B. tan
3
M. cossin 1 2
3
4 symbol fract
Math 140
Hw 21 Recommended problems, don't turn this in.
(1) Simplify using an addition formula (show the step
immediately after the addition formula). First point.
(2) Complete the simplification.
Second point.
Examples:
`sinx cosy x cosx siny x
sinx y
Math 140
Hw 22 Recommended problems, don't turn this in.
Evaluate the expressions.
A. sin
3
4
2
Picture for D and E.
.
5
b
First find cos q. The quadrant determines the sign.
q
4
D. (a) sin 2 (b) cos 2
(c) tan 2
(a) sin 2
E. (a) sin/2 (b) cos/2 (c) tan/
Math 140
Hw 20 Recommended problems, don't turn this in.
(1) Graph over one period (period doesn't have to start at 0).
(2) List the x-intercepts. (3) List both coordinates of the
highest and lowest points.
A. y sin3x First rewrite in the form Asin(B(x-C)
Math 140
Hw 23 Recommended problems, don't turn this in.
Write each expression as a sum or difference of
trigonometric functions. Don't calculate the answer.
L. 2 cos 2 cos 0
A. sin 20 cos 10
B. cos
5
C. sin
2
7
D. sin
7
12
cos
4
5
sin 5
7
cos
12
M. cos 2
Math 140
Hw 27 Recommended problems, don't turn this in.
E. 4, /6
C
b
A
a
B
c
A(a). sinB = 1/ 2 ,
What are the possible values, in degrees, for VB?
(b). cosB = 1/ 2 ,
What is the possible value, in degrees, for VB?
(c). sin A 1/4
What is the possible valu
Math 140
Hw 15
Recommended problems, don't turn this in.
Remember to include any needed units, e.g., mi/hr, rad/sec. Except
for 5ab, give only exact answers. No decimals.
A. Convert 45o to radian measure
I. A point (x,y) on the unit circle and on the term
Math 140
Hw 14
Recommended problems, don't turn this in.
Write N(t) in base e form. Then solve the problem.
A. A colony of bacteria starts with 2000 bugs. Two hours
later it has 3800.
N(t) =
(a) How many grams will remain after 48 hours?
(b) How long will
Math 140
Hw 13
Recommended problems, don't turn this in.
Simplify.
A. log 10 70 log 10 7
Express in terms of natural logarithms ln.
N. log 10 6.
B. log 7 7
O. log 10 e
C. log 3 108 log 3 3/4
D. 1 ln e
2
P. Solve for x using ln. 5 x 3 2x1 .
E. 2 log 2 5 3
Math 140
Hw 1
Recommended problems, don't turn in.
Find all real solutions x. Write Q if there are no solutions.
A. 3x 2 2 3x 2
N.
x1
x1
B. 3x 2 4x 3 0
O.
2x
32x
C. x 2 24
P.
x 2 8x9
x
D. xx 1 1
Q.
2x 3 5x 2 7x
3x 2 7x4
R.
x
x1
S
32x
32x
E.
1 2
2x
x 1 0
3
Math 140
Hw 6
Recommended problems, don't turn this in.
f(x)=2x-1, g(x)=x2-3x-6, h(x)=x3, k(x)=2, m(x)=x2-9.
A. (a) (f gx )
(b) f gx
(c) f g0
B. (a) m f x
Write each function as a composition
f g of simpler functions f and g.
F. (a) 3 3x 4
(b) |2x 3|
(c)
Math 140
Hw 3 Recommended problems, don't turn this in.
Divide to get the quotient q(x), remainder r(x). Write in
the form: px dxqx rx.
A.
x 2 8x4
x3
(b) 2fx.
(c) fx 2 .
x 2 6x2
B. x5
C.
(d) fx 2 .
6x 3 2x3
2x1
(e) fx/2.
(f) fx/2.
x 5 2
D. x3
x 6 64
E. x2
Math 140
Hw 2
Recommended problems, don't turn this in.
Find the center and radius.
A. x 3 2 y 1 2 25
B. x 2 y 2 2
C. x 2 y 2 8x 6y 24
K. (a) 1, 1, 1, 1
(b) 0, 5, 8, 5
(c) 1, 1, 1, 1
(d) a, b, b, a
Write the equations for the lines below in the one of the
Math 140
Hw 4
Recommended problems, continued.
In A-D, list the domain and range of each graph.
D. For the function f pictured,
4
A. For the function pictured,
3
2
1
4
-5
3
-4
-3
-2
-3
-2
4
5
-3
1
-1
3
-2
1
-4
2
-1
2
-5
1
-1
2
3
4
5
-1
(a) Is f(0) positiv
Math 140
Hw 12
Recommended problems, don't turn this in.
Rewrite each equation using logarithms rather than
exponentials (no decimal answers).
I. y log 3 x 2 1 See Hw 12 worked examples.
A. 9 3 2
B. 1000 10 3
C. 7 3 343
D.
2 2 1/2
Simplify to a rational n
Math 140
Hw 11
Recommended problems, don't turn this in.
A. Estimate as a power of 10:
(a) 2 30
(b) 2 50
y 3 x 1
In B-E: simplify to a number of the form bn.
B. 5
3
3
C. 4 1
2
41
2
2 4
D. 2 1
E. 5
J. Graph and on the graph mark the x-intercept,
y-intercep
Math 140
Hw 9
Recommended problems, don't turn this in.
Draw the picture; indicate your variables on the picture.
Write the equations which relate the variables.
Solve for the wanted quantities.
E. The hypotenuse of a right triangle is 20 cm. Express
the
Math 140
Hw 10
Recommended problems, don't turn this in.
Graph and on the graph mark the x and y-intercepts. Label the
degrees of the roots. No credit if the graph isn't smooth.
A. y x 3 4x 2 5x
B. y x 3 3x 2 4x 12
C. y x 3 x 2
D. y 2x 1x 4 3
J. y 3/x 2 2
Math 140
Hw 7
Recommended problems, don't turn this in.
A. fx 3x 1
(a) Find f 1 x
In E, F, G, graph the function. Circle 1-1 if 1-to-1;
circle not 1-1 if not.
F. y x 2 1
1-1?
not 1-1?
G. y 1/x
(c) Graph, y f x, y x, f f 1 x on same coordinate
system.
1-1?
Math 140
Hw 8
Recommended problems, don't turn this in.
v Write the function in the form: y ax h 2 k.
E.g., rewrite y x 1 2 as y x 1 2 0.
v List the roots.
v Graph. On the graph mark the vertex and give both coordinates .
A. y x 2 4x
v Draw the picture an
Math 140
Hw 26 Recommended problems, don't turn this in.
(a) Give the unsimplified exact answer obtained using the
law of sines or cosines or Straight V Thm. E.g.
a 8 2 5 2 285 cos20 0 or b
5 sin100 o
sin50 o .
An unsimplified exact answer for an angle mi