Download Practice Test 1

Name: ________________________ Class: ___________________ Date: __________
Practice Test1 (1600 Trigonometry)
ID: A
Instructor: Koshal Dahal
Multiple Choice Questions
SHOWȱALLȱWORK,ȱEVENȱFORȱMULTIPLEȱCHOICEȱQUESTIONS,ȱTOȱRECEIVEȱCREDIT.
____
1. Find the terminal point P (x, y) on the unit circle determined by t
13S
. Round each value to the nearest
2
hundredth.
a. (–0.00, –1.00)
b. (0.00, 1.00)
c. (0.00, –1.00)
d. (0.12, 1.14)
____
2. The point P is on the unit circle. The x-coordinate of P is
a.
b.
c.
d.
____
äå
ôõ
åå 1
õ
åå , 48 õõõ
åå 7
7 õõõ
å
æ
ö
äå 1 6 ôõ
åå , õõ
åå 7 7 õõ
æ
ö
ô
åäå 1
48 õõõõ
åå
åå ,
õ
åå 7
7 õõõ
æ
ö
äå
ôõ
åå 1
õ
åå , 48 õõõ
åå 7
7 õõõ
å
æ
ö
1
and P is in quadrant I. Find the point P(x, y).
7
2
3. The point P is on the unit circle. The x-coordinate of P is and P is in quadrant II. Find the point P (x, y).
7
äå
ôõ
åå 2
45 õõõ
õ
a. ååå ,
7 õõõ
åå 7
æ
ö
ô
åäå 2
45 õõõõ
å
õ
b. ååå ,
åå 7
7 õõõ
æ
ö
äå 2 5 ôõ
c. åååå , õõõõ
æ 7 7ö
ô
äå
åå 2
45 õõõõ
å
õ
d. åå ,
åå 7
7 õõõ
ö
æ
1
Name: ________________________
____
ID: A
4. Find the terminal point P (x, y) on the unit circle determined by t
S
5
. Round the values to the nearest
hundredth.
a. (0.93, 0.73)
b. (0.81, –0.59)
c. (–0.81, –0.59)
d. (0.81, 0.59)
____
5. Find the terminal point P (x, y) on the unit circle determined by t
S
. Round the values to the nearest
4
hundredth.
a. (0.71, –0.71)
b. (0.83, –0.85)
c. (–0.71, 0.71)
d. (–0.71, –0.71)
____
6. Find the terminal point P (x, y) on the unit circle determined by t
5S
. Round each value to the nearest
6
hundredth.
a. (0.87, –0.50)
b. (–0.87, –0.50)
c. (–0.99, 0.64)
d. (–0.87, 0.50)
____
åäå 4
å
7. Suppose that the terminal point determined by t is ååå ,
åå 7
æ
ôõ
äå
33 õõõ
åå 4
õ
a. ååå ,
åå 7
7 õõõ
ö
æ
äå
ô
åå
33 4 õõõõ
å
, õõ
b. åå 7
7 õõ
åå
æ
ö
ô
õ
åäå 4
33 õõõ
å
õ
c. ååå , åå 7
7 õõõ
ö
æ
ô
äå
åå 4
33 õõõõ
å
õ
d. åå , åå 7
7 õõõ
ö
æ
2
ô
33 õõõõ
õ . Find the terminal point determined by t S .
7 õõõ
ö
Name: ________________________
____
8. Find the reference number for t
a.
b.
c.
d.
____
S
ID: A
5S
.
4
5
5S
4
S
S
4
4
2S
. Round the coordinates of the
3
terminal point to the nearest hundredth, and express the reference number in terms of S
9. Find the terminal point P (x, y) and the reference number determined by t
S
a.
terminal point is (–0.50, 0.87), reference number is
b.
terminal point is (–0.50, –0.87), reference number is
c.
terminal point is (0.50, –0.87), reference number is
d.
terminal point is (0.50, 0.87), reference number is
3
S
S
3
3
2S
3
5S
. Round the coordinates of
6
the terminal point to the nearest hundredth, and express the reference number in terms of S
____ 10. Find the terminal point P (x, y) and the reference number determined by t
a.
b.
terminal point is (0.87, –0.50), reference number is
S
6
5S
terminal point is (–0.87, –0.50), reference number is
6
c.
terminal point is (–0.87, –0.50), reference number is
d.
terminal point is (–0.87, 0.50), reference number is
S
S
6
6
19S
. Round the coordinates of
6
the terminal point to the nearest hundredth, and express the reference number in terms of S
____ 11. Find the terminal point P (x, y) and the reference number determined by t
a.
b.
terminal point is (–0.87, 0.50), reference number is
S
6
5S
terminal point is (–0.87, –0.50), reference number is
6
S
c.
terminal point is (0.87, –0.50), reference number is
d.
terminal point is (–0.87, –0.50), reference number is
3
6
S
6
Name: ________________________
ID: A
61S
. Round the coordinates of
6
the terminal point to the nearest hundredth, and express the reference number in terms of S
____ 12. Find the terminal point P (x, y) and the reference number determined by t
a.
terminal point is (–0.87, 0.50), reference number is
b.
terminal point is (0.87, –0.50), reference number is
c.
d.
S
6
S
6
5S
terminal point is (–0.87, –0.50), reference number is
6
terminal point is (–0.87, –0.50), reference number is
S
6
____ 13. Find the exact values of the trigonometric functions sin2S and cos 2S .
a. sin2S 1, cos 2S 0
b. sin2S 1, cos 2S 1
c. sin2S 0, cos 2S 1
____ 14. Find the exact value of the trigonometric functions sin
a.
b.
c.
13
S
2
13
sin S
2
13
sin S
2
sin
11
S
2
11
1, sin S
2
11
0, sin S
2
1, sin
13
11
S and sin S .
2
2
0
1
1
9
9
____ 15. Find the exact values of the trigonometric functions sin S and cos S .
4
4
a.
9
sin S
4
b.
9
sin S
4
c.
9
sin S
4
3
9
, cos S
2
4
1
9
, cos S
2
4
2
9
, cos S
2
4
3
2
3
2
2
2
7
1
____ 16. Find the exact values of the trigonometric functions sin S and sin S .
6
6
7
1
a. sin S 0.5, sin S 0.5
6
6
7
1
b. sin S 0.5, sin S 0.5
6
6
7
1
c. sin S 0.5, sin S 0.5
6
6
4
Name: ________________________
ID: A
____ 17. Find the exact values of the trigonometric functions sec
a.
b.
c.
13
S
3
13
sec S
3
sec
sec
13
7
S and csc S .
3
3
2 3
7
S
3
3
7
3 , cot S 2
3
2, csc
13
S
3
3, csc
3
3
7
S
3
____ 18. Find the exact values of the trigonometric functions sec 9S and csc
a.
sec 9S
b.
sec 9S
c.
sec 9S
1
S
2
1
1, csc S
2
1
1, csc S
2
1, csc
1
S.
2
1
1
5
11
____ 19. Find the exact values of the trigonometric functions tan S and tan S .
4
4
a.
b.
c.
2
11
, tan S
2
4
5
tan S
4
2
2
3
3
11
, tan S 2
2
4
11
1, tan S 1
4
5
tan S
4
5
tan S
4
____ 20. Find the exact value of the trigonometric function cos
a.
b.
c.
15
S
2
15
cos S
2
15
cos S
2
cos
15
S.
2
1
0
1
ô
åäå 1
0 õõõõ
å
õ . Find sin t, cos t, and tan t.
____ 21. The terminal point determined by t is ååå ,
åå 1
1 õõõ
æ
ö
0
1
0
a. sin t
, cost , tan t
1
1
1
b.
sint
c.
sint
1
, cost
1
0
, cost
1
0
, tant
1
1
, tant
1
0
1
0
1
5
Name: ________________________
ID: A
ô
åäå 3
7 õõõõ
å
õ . Find sin t, cos t, and tan t.
____ 22. The terminal point determined by t is ååå ,
åå 4 4 õõõ
æ
ö
7
3
7
a. sint
, cost
, tan t
4
4
3
b.
sint
3
, cost
4
7
, tant
4
7
3
c.
sint
7
, cost
4
3
, tant
4
7
3
5
and the terminal point of t is in quadrant II.
3
____ 23. Find the values of the trigonometric functions of t if sin t
a.
sint
5
, cost
3
2
, tan t
3
b.
sin t
5
, cost
3
2
, tan t
3
c.
sint
5
, cost
3
5
, tan t
3
5
, cot t
2
2 5
5
2 5
5
5
, cot t
2
5
, cot t
2
2 5
5
____ 24. Find the values of the trigonometric functions of t if cost
a.
sint
64
, cost
10
6
, tan t
10
b.
sint
64
, cost
10
6
, tant
10
c.
sint
64
, cost
10
64
, cot t
6
64
, cot t
6
64
, cot t
6
6
, tan t
10
6 64
64
6 64
64
6 64
64
____ 25. Find the values of the trigonometric functions of t if sec t
a.
sin t
b.
sin t
c.
sin t
0
, cost
1
0
, cost
1
0
, cost
1
1
, tan t
1
1
, tan t
1
0
, tan t
1
0
, cot t
1
1 0
0
0
, cot t
1
0
, cot t
1
1 0
0
1 0
0
6
6
and the terminal point of t is in quadrant III.
10
1
, and the terminal point of t is in quadrant IV.
1
Name: ________________________
ID: A
____ 26. Find the values of the trigonometric functions of t if tant
a.
sint
6
, cost
24
b.
sint
c.
sint
6
, cost
24
6
, cost
24
540
, tant
24
4, cot t
1
4
540
, tant
24
4, cot t
1
4
540
, tant
24
1
4
4, cot t
____ 27. Find the values of the trigonometric functions of t if tant
11
, cost
6
5
, tan t
6
11
, cot t
5
4 and the terminal point of t is in quadrant II.
11
and cos t ! 0.
5
5 11
11
a.
sint
b.
sint
11
, cost
6
5
, tan t
6
11
, cot t
5
5 11
11
c.
sint
11
, cost
6
5
, tan t
6
11
, cot t
5
5 11
11
____ 28. Find the values of the trigonometric functions of t if sin t
a.
sint
13
, cost
7
13
, tan t
7
13
, cot t
6
6 13
13
b.
sint
13
, cost
7
6
, tan t
7
13
, cot t
6
6 13
13
c.
sint
13
, cost
7
6
, tant
7
13
and sec t 0.
7
6 13
13
13
, cot t
6
____ 29. Determine whether the function 9x 2 cos x is even, odd, or neither.
a. odd
b. even
c. neither
____ 30. Determine whether the function |5x| cos 2x is even, odd, or neither.
a. neither
b. odd
c. even
7
Name: ________________________
ID: A
____ 31. Graph the function.
g(x)
7cos x
a.
d.
b.
e.
c.
8
Name: ________________________
ID: A
____ 32. Graph the function.
g(x)
6sinx
a.
d.
b.
e.
c.
9
Name: ________________________
ID: A
____ 33. Graph the function.
g(x)
6 6cos x
a.
c.
b.
d.
10
Name: ________________________
ID: A
____ 34. Graph the function.
g(x)
4 3sinx
a.
d.
b.
e.
c.
11
Name: ________________________
ID: A
____ 35. Sketch the graph.
y
5 cos
1
x
3
a.
d.
b.
e.
c.
12
Name: ________________________
ID: A
____ 36. Find the period and graph the function.
y 2tan x
a. period 2S
d.
period S
b.
period 2S
e.
period S
c.
period S
13
Name: ________________________
ID: A
____ 37. Find the period and graph the function.
y
äå
S ôõ
tan ååå x õõõõ
åæ
4ö
14
Name: ________________________
ID: A
a.
period 2S
d.
period S
b.
period S
e.
period S
c.
period 2S
15
Name: ________________________
ID: A
åä S õô
åä S
____ 38. Find the exact value of sin åååå õõõõ and cos åååå æ2ö
æ 2
åä S õô
åä S õô
a. sin åååå õõõõ 0, cos åååå õõõõ 1
æ2ö
æ 2ö
åä S õô
åä S õô
b. sin åååå õõõõ 1, cos åååå õõõõ 0
æ2ö
æ 2ö
äå S ôõ 1
äå S ôõ 3
c. sin åååå õõõõ
, cos åååå õõõõ
æ2ö 2
æ 2ö 2
äå S ôõ
äå S ôõ
d. sin ååå õõõ 1, cos ååå õõõ 1
åæ 2 õö
åæ 2 õö
äå S ôõ
äå S ôõ
e. sin åååå õõõõ 1, cos åååå õõõõ 0
æ2ö
æ 2ö
äå 7S
____ 39. Find the exact value of sec ååå
åæ 4
b.
c.
e.
ôõ
ä
õõ and csc ååå 17S
õõ
åå 4
ö
æ
ôõ
õõ .
õõ
ö
2 2
,
3
3
1
2,
2
2, 2
a.
d.
õôõ
õõ .
õ
ö
2
, 2
2
1, 1
____ 40. Find the exact value of the expression, if it is defined.
ä
ä
cos åååå tan 1 ååå
æ
æ
a.
b.
c.
d.
e.
ôô
3 õõõ õõõõ
öö
1
2
3
2
45
1
2
none of these
16
Name: ________________________
ID: A
____ 41. Find the approximate value of cos &1.8' using a calculator.
0.14
0.23
0.69
0.51
0.85
a.
b.
c.
d.
e.
____ 42. Find the exact value of the expression, if it is defined.
äå
ô ôõ
åå 1 äååå
2 õõõõ õõõ
å
å
cot ååå cos åå õõ
åå 2 õõõ õõõõ
åå
æ
öö
æ
1
2
45
1
1
2
a.
b.
c.
d.
none of these
e.
____ 43. Find the exact value of each expression, if it is defined.
äå
ô
åå
2 õõõõ
å
sin åå õ
åå 2 õõõ
æ
ö
1
a.
b.
c.
d.
e.
S
S
3
2
S
S
4
4
S
3
17
Name: ________________________
ID: A
Numeric Response
÷
ç
44. Find all solutions of the equation that lie in the interval èèé 0, S øøù . State each answer correct to two decimal
places.
cos x
0.9
x = __________
Short Answer
45. The point P is on the unit circle. Find P(x, y) from the given information.
The y-coordinate of P is
10
and the x-coordinate is negative.
11
46. The point P is on the unit circle. Find P(x, y) from the given information.
The x-coordinate of P is positive and the y-coordinate of P is 10
.
10
47. Find the terminal point P(x, y) on the unit circle determined by the given value of t
4S
.
3
48. Find the terminal point P(x, y) on the unit circle determined by the given value of t
5S
.
3
18
Name: ________________________
ID: A
49. Find the approximate value of the given trigonometric function.
sin 1
(a) By using the figure. Please give the answer to one decimal place.
sin 1
__________
(b) By using a calculator in radians. Please give the answer to five decimal places.
sin 1
__________
÷
ç
50. Find all solutions of the equation that lie in the interval èèé 0, S øøù . State each answer correct to two decimal
places.
csc x
11
x = __________
19
Name: ________________________
ID: A
51. Each time your heart beats, your blood pressure first increases and then decreases as the heart rests between
beats. The maximum and minimum blood pressures are called the systolic and diastolic pressures,
respectively. Your blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered
normal.
A certain person's blood pressure is modeled by the function
p(t)
110 15sin(150S t)
where p (t) is the pressure in mmHg, at time t measured in minutes.
(a) Find the period of p.
period = __________ minute
(b) Find the number of heartbeats per minute.
(c) Find the blood pressure reading.
__________ / __________
(d) How does this compare to normal blood pressure?
20