Exam 1
-
Chapter 4
Name:
Instructions:
Justify each answer.
Record your answer in the answer fields.
Each answer has equal weight.
1.
10.
2.
11.
3.
12.
4.
13.
5.
14.
6.
15.
7.
16.
8.
17.
9.
18.
19.
Period =
Amplitude
=
Phase
shift=
20.
sin(O)
cos(O)
tan (&)
sec(O)
cot(s)
1
‘I
/1
k!
csc(9)
mi>IIi
ir
2ir
—2ir
21.
arccos(9)
arcsin(E)
arctan(O)
if
if
2
2
1/2
i
—1
—1/2
1/2
1
2
-If
-if
-if
ir
27r
-J
“k,
radians. Find two coterminal angles in radians, one
1. Suppose 0 =
positive and one negative.
—
c)
4-
II
(0
—if
£
(.L
.13
-3
‘C-
2. Suppose 0
-
radialls. Convert the angle to degrees.
=
3. A disc with radius 5 cm spins 15 revolutions per minute. Give the
angular speed in radians per minute and the linear speed in cm per
minute.
--‘
I
I
Ee/
.kLI./
I
“s
For
#4
to
#9,
use
the picture below.
-z
9
(-i=
92
What
are
the
values
(7, —12)
for the
six trigonometric
functions for
this
.
tz
sin(O)
=
5. cos(O)
=
6. tan(O)
=
7. csc(O)
=
8. sec(9)
=
9. cot(O)
=
4.
For #10
-y
to
i1’
II-
#14,
suppose
What are the other
cos(0)
;
..‘.
=
—
11
3
and csc(O) <0.
)
five trigonometric function va1es
for
this 0?
—5
V
10. sin(0)
=
11. tan(0)
=
12. csc(0)
=
13. sec(0)
=
14. cot(0)
=
—
Cj
-
-
-f4g
IL
-
-
V
1) \
:1
c;LcL7
15. Suppose that U
=
209°. What number is the reference angle in degrees?
a9
O9
16. In which of the four quadrants does U lie when sin(9)
Ic
cot(O) <0?
17. Suppose sin(U)
00 and 360°?
=
.
>
0 and
What are two different numbers for 0 between
t2C
18. What is the exact value of
tan (arccos
(s))?
5
19. Find the period, amplitude, and phase shift of the function f(x)
a sin (bx + c) graphed below.
3
=
Lf((
(5
2
1
—3ir
—2ir
—2
ir“Lk
w5
—3
or
;CQ•
20. Sketch a graph of sin, cos, tan, csc, sec, cot.
21. Sketch a graph of aresin, arccos, aretan.
22. Sketch a graph for f(O)
=
2cos(O+
).
4
3
3ir
2
—2
—4
2ir
47r
radians. Find
1. Suppose U =
positive and one negative.
—---
two
coterminal angles in radians, one
7—Zr
7
2. Suppose U
7ir
=
radians. Convert the angle to degrees.
IF
3. A disc with radius 4 cm spins 25 revolutions per minute. Give the
angular speed in radians per minute and the linear speed in cm per
minute.
SQir
--
C)J
V
I
rJ
oO r
rxzL
For #4 to #9, use the picture below.
(--) (
F)
R
6
(—9, —2)
What are the values for the six trigonometric functions for this
&.
—
4.
sin(9) =
5.
cos(6)
6.
tan(O) =
=
-
7. csc(O)
=
8. sec(6)
=
9. cot(O)
=
I
For #10 to #14, suppose sec(0)
11
=
—--
and sin(O) > 0.
cc
What are the other five trigoi1dmetric function values for
a
this 0?
‘
10. sin(0)
11. tan(0)
\,
‘\
=
=
12. csc(0)
=
13. sec(0)
=
14. cot(0)
=
ty
LI/
—S
C5/
—
u
1
*
‘1
2
C(A
15. Suppose that 0
=
243°. What number is the reference angle in degrees?
16. In which of the four quadrants does 9 lie when csc(9) <0 and
tan(9) > 0?
17. Suppose sin(9)
0° and 360°?
=
—.
What are two different numbers for 9 between
J
18. What is the exact value of
sin (arctan
())?
H
19. Find the period, amplitude, and phase shift of the function f(x)
a sin (bx + c) graphed below.
r
-
=
Z
—
—
—3
20. Sketch a graph of sin, cos, tan, csc, sec, cot.
21. Sketch a graph of arcsin, arccos, arctan.
22. Sketch a graph for f(&)
I
=
—4sin
(o +
I
I
4I2
r Ti