Name: __________________
1
Class:
Date: _____________
Find the numerical value of each expression.
(a) sinh (ln 2)
(b) sinh 3
Problem
code:
stet.
03.09.03
If sinh x =
2
4 , find the values of the other hyperbolic functions at x.
3
<span onSplitBottomComment="<i>..to be continued</i>" onSplitUpperComment="continuation" class="choices">
Problem
code: stet.
03.09.20m
PAGE 1
a. csch x =
3 , cosh x = 4 , sech x = 5 , tanh x = 1 , coth x = 3
4
5
4
3
5
b. csch x =
4 , cosh x = 3 , sech x = 5 , tanh x = 5 , coth x = 4
3
5
3
4
5
c. csch x =
3 , cosh x = 5 , sech x = 3 , tanh x = 4 , coth x = 5
4
3
5
5
4
d. csch x =
3 , cosh x = 5 , sech x = 1 , tanh x = 3 , coth x = 5
4
4
5
5
4
e. csch x =
4 , cosh x = 5 , sech x = 4 , tanh x = 3 , coth x = 5
3
4
5
5
3
Name: __________________
If tanh x =
3
Class:
Date: _____________
3 , find the values of the other hyperbolic functions at x.
5
5 , sech x =
3
sinh x = 3 , csch x =
4
4 , cosh x = 5 ,
5
4
4
3
3 , sech x =
5
sinh x = 4 , csch x =
3
5 , cosh x = 4 ,
4
5
3
4
5 , sech x =
3
sinh x = 5 , csch x =
4
4 , cosh x = 1 ,
3
4
4
3
a. coth x =
b. coth x =
c. coth x =
5 , sech x = 3 , cosh x = 4 ,
3
4
3
1
5
sinh x =
, csch x =
5
4
d. coth x =
3 , sech x =
5
sinh x = 5 , csch x =
4
e. coth x =
4 , cosh x = 3 ,
3
4
4
5
Problem
code: stet.
03.09.21m
4
Which of the following formulas are proven correctly?
Select all correct answers.
Problem
code: stet.
03.09.24m
PAGE 2
2
2
d coth x = d
dx
dx
sinh x
cosh x
1
= cosh x cosh x sinh x sinh x = cosh x sinh x =
= 2
2
2
cosh x
cosh x
cosh x
b.
d cosh x = d
dx
dx
1
sinh x
= cosh x = 2
sinh x
1
cosh x = sinh x
sinh x sinh x
c.
d csch x = d
dx
dx
1
sinh x
= cosh x = 2
sinh x
1
cosh x = sinh x sinh x
d.
d sech x = d
dx
dx
1
cosh x
= e.
d csch x = d
dx
dx
1 ex + e
2
a.
(
x
sinh x = 2
cosh x
)
(
x
= 1 e 2
1
sinh x = cosh x cosh x
x
e
) = sinh x
csch x coth x
sech x tanh x
1
2
sinh x
Name: __________________
5
Class:
Date: _____________
A telephone line hangs between two poles 16 m apart in the shape of the catenary y = 50 cosh
are measured in meters.
(a) Find the slope of this curve where it meets the right pole.
Please round the answer to four decimal places.
________
(b) Find the angle between the line and the pole.
Please round the answer to two decimal places.
________
Problem
code:
stet.
03.09.49
6
Problem
code:
stet.
03.09.53
PAGE 3
At what point of the curve y = cosh x does the tangent have slope 2?
x
50
45 , where x and y
ANSWER KEY
Homework 3.9 Math 19A Fall 2006, Bauerle
1.
3 ;
4
10.01787
ANSWER KEY 2. c
Page 1
3. a
4. c,d
5.
0.1607
80.87
( (
)
6. ln 2+ 5 , 5
)