Deck 20: Trigonometry With Any Angle

Question 1

Find the angle of the vector with endpoints (-3, -3).

Answer 1

225°

Question 2

Find the magnitude of the vector in standard position with end point (5, 8).

A)9.4
B)5
C)13
D)89

Answer 2

A

Question 3

Find the length of the vector whose endpoint is: (9, 12)

Answer 3

15 units

Question 4

Find the direction of the vector whose end point coordinates are (-5, -11).

A)24.4°
B)-24.4°
C)245.6°
D)-65.6°

Question 5

Find the angle of the vector whose endpoint is: (6, -6)

Question 6

Find the magnitude of the vector in standard position with end point (-4, 9).

A)9.8
B)3.2
C)5.1
D)8.1

Question 7

Find the magnitude of the vector in standard position with end point (-3, -7).

A)7.6
B)4.5
C)5.0
D)6.3

Question 8

Find the length of the vector whose endpoint is: (-5, 5)

Question 9

Find the length of the vector whose endpoint is: (5, 12)

Question 10

Find the magnitude of the vector in standard position with end point (5, -2).

A)4.6
B)6.4
C)1.5
D)5.4

Question 11

Find the direction of the vector in standard position with end point (15, 25). Round to the nearest hundredth.

A)84.29°
B)30.96°
C)59.04°
D)53.13°

Question 12

Find the magnitude of the vector in standard position with end point (8.4, 2.7).

A)11.1
B)8.8
C)4.7
D)8.0

Question 13

Find the length of the vector whose endpoint is: (4, -4)

Question 14

Find the direction of the vector in standard position with end point (2, 7). Round to the nearest hundredth.

A)16.60°
B)74.05°
C)0.02°
D)15.95°

Question 15

Find the direction of the vector in standard position with end point (12, 5). Round to the nearest hundredth.

A)67.38°
B)24.62°
C)22.62°
D)65.38°

Question 16

Find the direction of the vector in standard position with end point (6, 8). Round to the nearest hundredth.

A)53.13°
B)41.41°
C)48.59°
D)36.87°

Question 17

Find the direction in degrees (to the nearest 0.1°)of the vector It (total current)in the given figure.

A)52.1°
B)37.9°
C)51.1°
D)38.9°

Question 18

Find the direction of the vector in standard position with end point (8, 3). Round to the nearest hundredth.

A)69.44°
B)22.02°
C)67.98°
D)20.56°

Question 19

Find the magnitude of the vector whose end point coordinates are (-7, 15).

A)16.6
B)8
C)13.3
D)22

Question 20

Find the magnitude of the vector in standard position with end point (2, 6).

A)5.7
B)7.2
C)6.3
D)4

Question 21

Find the direction in degrees of a vector in standard position if the coordinates of its end point are (-3, 7). Round to the nearest 0.1°.

A)-66.8°
B)66.8°
C)113.2°
D)-113.2°

Question 22

Find the related angle for 336°.

A)24°
B)66°
C)-24°
D)156°

Question 23

Find the sum of two vectors if one has a direction of 52° and a magnitude of 12 and the other has a direction of 30° and a magnitude of 8.

A)magnitude of 19.65 with a direction of 46.8°
B)magnitude of 19.65 with a direction of 41°
C)magnitude of 19.65 with a direction of 43.2°
D)magnitude of 14.42 with a direction of 41°

Question 24

Find the sum of two vectors if one has a direction of 65° and a magnitude of 10, and the other has a direction of 35° and a magnitude of 15.

A)magnitude of 25 at direction of 100°
B)magnitude of 5 at direction of 30°
C)magnitude of 24.2 at direction of 46.9°
D)magnitude of 24.2 at direction of 100°

Question 25

Two forces with magnitude of 45.3 pounds and 56.4 pounds act on a machine part at 85° and 32°, respectively. Find the direction and magnitude of the resultant of these two forces.

A)91.2 pounds at 61.6°
B)101.7 pounds at 117°
C)101.7 pounds at 55.4°
D)91.2 pounds at 117°

Question 26

Find the magnitude and direction of the resultant of the sum of 2 + 3i and 4 + 7i which are in complex notation.

A)8.00 with direction of 31.0°
B)11.66 with direction of 59.0°
C)5.66 with direction of 59.0°
D)11.66 with direction of 31.0°

Question 27

Find the direction in degrees of a vector in standard position if the coordinates of its end point are (-3, 7). Round to the nearest 0.1°.

A)113.2°
B)66.8°
C)-66.8°
D)-113.2°

Question 28

Find the magnitude and direction of the resultant of the sum of 1 + 4i and 2 + 5i which are in complex notation.

A)8.49 with direction of 71.6°
B)9.49 with direction of 71.6°
C)9.49 with direction of 18.4°
D)8.49 with direction of 18.4°

Question 29

Find the related angle for 200°.

A)-20°
B)20°
C)380°
D)160°

Question 30

Find the polar coordinates of a vector in standard notation that has polar coordinates of (1.2, 60°). Round to tenths.

A)(1.1, 0.4)
B)(1.0, 0.6)
C)(0.6, 1.0)
D)(-1.1, -0.4)

Question 31

Find the polar coordinates of a vector in standard notation that has rectangular coordinates of (-2, 4). Report the angle coordinate in radians.

A)(-4.5, -26.6°)
B)(-4.5, 63.4°)
C)(4.5, -63.4°)
D)(3.5, 0.03°)

Question 32

Find the resultant vector of two vectors that have a direction of 48° and magnitudes of 6 and 2, respectively.

A)magnitude of 8 with direction of 0°
B)magnitude of 4 with direction of 48°
C)magnitude of 8 with direction of 48°
D)magnitude of 16 with direction of 48°

Question 33

Find the polar coordinates of a vector in standard notation that has rectangular coordinates of (1, 4).

A)(1.7, 76.0°)
B)(4.1, 76.0°)
C)(4.1, 14.0°)
D)(1.4, 48.6°)

Question 34

Find the direction of the vector in standard position with end point (3, 11). Round to the nearest hundredth.

A)15.83°
B)15.26°
C)74.17°
D)74.74°

Question 35

Two forces with magnitude of 2,000 pounds and 900 pounds act on a machine part at 105° and 30°, respectively. Find the direction and magnitude of the resultant of these two forces.

A),900 pounds at 83.7°
B)2,900 pounds at 135°
C)1,100 pounds at 75°
D)2,396.2 pounds at 83.7°

Question 36

Find the resultant vector of two vectors that have a direction of 32° and magnitudes of 8 and 16, respectively.

A)24 at 32°
B)8 at 0°
C)128 at 32°
D)24 at 0°

Question 37

Find the sum of two vectors if one has a direction of 37° and a magnitude of 15 and the other has a direction of 217° and a magnitude of 9.

A)magnitude of 24 with direction of 217°
B)magnitude of 6 with direction of 217°
C)magnitude of 6 with direction of 37°
D)magnitude of 24 with direction of 37°

Question 38

Find the polar coordinates of a vector in standard notation that has polar coordinates of (4, 30°). Round to tenths.

A)(0.6, -4.0)
B)(3.5, 2)
C)(0.6, 2)
D)(3.5, 30°)

Question 39

Find the related angle for 120°.

A)60°
B)240°
C)-60°
D)20°

Question 40

A)(0.04, 2.0)
B)(1.7, 1)
C)(2.0, 0.04)
D)(1, 1.7)

Question 41

Give the signs of the sine, cosine, and tangent trigonometric functions of the vector with the endpoint (-4, 4)

A)sine, positive; cosine, negative; tangent, positive
B)sine, positive; cosine, negative; tangent, negative
C)sine, positive; cosine, positive; tangent, positive
D)sine, negative; cosine, negative; tangent, negative

Question 42

Sam measures a 30 degree angle between a flagpole and a tree. If Sam measured 20 m between himself and the tree and there is a 90 degree angle from the tree to the flagpole and Sam, how far away is the tree from the flagpole?

A)20 m
B)10 m
C)11.5 m
D)17.3 m

Question 43

Find the value of cos 2.45 rad. Round to four significant digits.

A)0.9991
B)-0.7702
C)0.6378
D)-0.8280

Question 44

Find the related angle for 5.92 rad. Use the calculator value for n and round to hundredths.

A)-0.36 rad
B)0.36 rad
C)-1.21 rad
D)2.78 rad

Question 45

Using a calculator, find the value of sin 250°. Round to four significant digits.

A)1.0642
B)-0.9397
C)0.9397
D)-1.0642

Question 46

Find the related angle for 245°.

A)65°
B)0°
C)25°
D)180°

Question 47

Find the value of the sin 156°.

Question 48

Give the signs of the three trigonometric functions of the vector with the endpoint (2, 8).

A)sine, positive; cosine, negative; tangent, positive
B)sine, positive; cosine, positive; tangent, positive
C)sine, negative; cosine, positive; tangent, positive
D)sine, negative; cosine, negative; tangent, negative

Question 49

Find the related angle for 2.06 rad. Use the calculator value for n and round to hundredths.

A)4.22 rad
B)-1.08 rad
C)2.65 rad
D)1.08 rad

Question 50

Give the signs of the three trigonometric functions of the vector with the endpoint (-3, 5).

A)sine, negative; cosine, positive; tangent, positive
B)sine, positive; cosine, positive; tangent, negative
C)sine, positive; cosine, negative; tangent, positive
D)sine, positive; cosine, negative; tangent, negative

Question 51

Using a calculator, find the value of sin 4.2. Round to four significant digits.

A)0.9973
B)0.8716
C)-0.9973
D)-0.8716

Question 52

Find the value of the cos 265°.

Question 53

Find the value of the sin 325°.

Question 54

Using a calculator, find the value of sin 4.7. Round to four significant digits.

A)-0.9999
B)0.9966
C)0.08193
D)-0.01239

Question 55

Find the value of the cos 123°.

Question 56

Find the value of sin 263°. Round to four significant digits.

A)-0.7794
B)0.6265
C)-0.9925
D)0.9684

Question 57

Give the signs of the three trigonometric functions of the vector with the endpoint (-4, -7).

A)sine, positive; cosine, positive, tangent, positive
B)sine, negative; cosine, negative, tangent, positive
C)sine, negative; cosine, positive, tangent, negative
D)sine, negative; cosine, negative, tangent, negative

Question 58

Give the signs of the three trigonometric functions of the vector with the endpoint (4, -1).

A)sine, positive; cosine, negative; tangent, negative
B)sine, negative; cosine, positive; tangent, negative
C)sine, negative; cosine, negative; tangent, negative
D)sine, positive; cosine, negative; tangent, positive

Question 59

Give the sign of the three trigonometric functions of the vector with the endpoint (0, 5).

A)sine, negative; cosine, positive; tangent, positive
B)sine, positive; cosine, negative; tangent, positive
C)sine, positive; cosine, zero; tangent, undefined
D)sine, zero; cosine, positive; tangent, zero

Question 60

Find the value of tan 326°. Round to four significant digits.

A)-0.6745
B)-0.8871
C)-0.6235
D)0.6745

Question 61

What is the amplitude for the function y = 3 sin 2x?

A)2
B)6x
C)3
D)2x

Question 62

What is the amplitude of the function

A)5
B)-45°
C)2
D)45°

Question 63

What is the amplitude of the function y = (3x +180°)?

A) 180°
B) 3x
C) 3
D) 1/3

Question 64

Using a calculator, find the value of tan 3.5. Round to four significant digits.

A)0.3746
B)-0.06116
C)0.06116
D)-0.3746

Question 65

Using a calculator, find the value of cos 195°. Round to four significant digits.

A)0.9659
B)-0.9756
C)-0.9659
D)0.9756