Chapter 7

Question 0

Clockwise Angle Rotation

Answer 0

Negative

Question 1

Counterclockwise Angle Rotation

Answer 1

Positive

Question 2

Standard Position

Answer 2

If an angle has its vertex at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

Question 3

Arc Length Formula

Answer 3

For a circle of radius r, a central angle of theta radians subtends an arc whose length s is
S=r(theta)

Question 4

1 revolution (radians)

Answer 4

2pi

Question 5

180 degrees (radians)

Answer 5

pi

Question 6

1 degree (radians)

Answer 6

pi/180

Question 7

1 radian (degree)

Answer 7

180/pi

Question 8

0 degree (radians)

Answer 8

0

Question 9

30 degree (radians)

Answer 9

pi/6

Question 10

45 degree (radians)

Answer 10

pi/4

Question 11

60 degree (radians)

Answer 11

pi/3

Question 12

90 degree (radians)

Answer 12

pi/2

Question 13

120 degree (radians)

Answer 13

2pi/3

Question 14

135 degree (radians)

Answer 14

3pi/4

Question 15

150 degree (radians)

Answer 15

5pi/6

Question 16

180 degree (radians)

Answer 16

pi

Question 17

210 degree (radians)

Answer 17

7pi/6

Question 18

225 degree (radians)

Answer 18

5pi/4

Question 19

240 degree (radians)

Answer 19

4pi/3

Question 20

270 degree (radians)

Answer 20

3pi/2

Question 21

300 degree (radians)

Answer 21

5pi/3

Question 22

315 degree (radians)

Answer 22

7pi/4

Question 23

330 degree (radians)

Answer 23

11pi/6

Question 24

360 degree (radians)

Answer 24

2pi

Question 25

Area of Sector

Answer 25

The area A of the sector of a circle of radius r formed by a central angle of theta radians is A=(1/2)*r*r*(theta)

Question 26

Linear Speed

Answer 26

Suppose that an object moves around a circle of radius r at a constant speed. If s is the distance traveled in time t around this circle, then the linear speed v of the object is defined as v=s/t

Question 27

Angular Speed

Answer 27

The angular speed omega of this object is the angle theta (rad) swept out, divided by the elapsed time t; that is, omega=theta/t

Question 28

Linear Speed

Answer 28

v=r(omega)

Question 29

In standard position, b is

Answer 29

the side farthest away from the angle

Question 30

In standard position, a is

Answer 30

the side adjacent to the angle

Question 31

In standard position, c or r is

Answer 31

The hypotenuse

Question 32

Sin(theta)

Answer 32

b/c

Question 33

Cos(theta)

Answer 33

a/c

Question 34

Tan(theta)

Answer 34

b/a

Question 35

Csc(theta)

Answer 35

c/b

Question 36

Sec(theta)

Answer 36

c/a

Question 37

Cot(theta)

Answer 37

a/b

Question 38

SOHCAHTOA

Answer 38

``` Sin Opposite over Hypotenuse Cos Adjacent over Hypotenuse Tan Opposite over Adjacent ```

Question 39

Reciprocal Identities

Answer 39

csc(theta)=1/sin(theta) sec(theta)=1/cos(theta) cot(theta)=1/tan(theta)

Question 40

Quotient Identities

Answer 40

tan(theta)=sin(theta)/cos(theta) | cot(theta)=cos(theta)/sin(theta)

Question 41

sin^2(theta)+cos^2(theta)=

Answer 41

1

Question 42

tan^2(theta)+1=

Answer 42

sec^2(theta)

Question 43

cot^2(theta)+1=

Answer 43

csc^2(theta)

Question 44

Complementary Angles Theorem

Answer 44

Cofunctions of complementary angles are equal.

Question 45

sin is cofunctions with

Answer 45

cos

Question 46

sec is cofunctions with

Answer 46

csc

Question 47

tan is cofunctions with

Answer 47

cot

Question 48

function(theta)=

Answer 48

cofunction(90-theta)

Question 49

sin30deg

Answer 49

1/2

Question 50

cos30deg

Answer 50

root3/2

Question 51

tan30deg

Answer 51

root3/3

Question 52

csc30deg

Answer 52

2

Question 53

sec30deg

Answer 53

2*root3/3

Question 54

cot30deg

Answer 54

root3

Question 55

sin and cos 45deg

Answer 55

root2/2

Question 56

tan and cot 45deg

Answer 56

1

Question 57

sec and csc 45deg

Answer 57

root2

Question 58

sin60deg

Answer 58

root3/2

Question 59

cos60deg

Answer 59

1/2

Question 60

tan60deg

Answer 60

root3

Question 61

csc60deg

Answer 61

2*root3/3

Question 62

sec60deg

Answer 62

2

Question 63

cot60deg

Answer 63

root3/3

Question 64

Angle of Depression

Answer 64

The acute angle made by the line of sight to the object and the horizontal when a person is looking up or down.

Question 65

In standard position, sin(theta)

Answer 65

b/r

Question 66

In standard position, cos(theta)

Answer 66

a/r

Question 67

In standard position, tan(theta)

Answer 67

b/a

Question 68

In standard position, csc(theta)

Answer 68

r/b

Question 69

In standard position, sec(theta)

Answer 69

r/a

Question 70

In standard position, cot(theta)

Answer 70

a/b

Question 71

Coterminal Angles

Answer 71

Angles in standard position that have the same terminal side.

Question 72

Quadrant 1

Answer 72

``` sin, csc positive cos, sec positive tan, cot positive ```

Question 73

Quadrant 2

Answer 73

``` sin, csc positive cos, sec negative tan, cot negative ```

Question 74

Quadrant 3

Answer 74

``` sin, csc negative cos, sec negative tan, cot positive ```

Question 75

Quadrant 4

Answer 75

``` sin, csc negative cos, sec positive tan, cot negative ```

Question 76

Reference Angle

Answer 76

The acute angle formed by the terminal side and the x-axis

Question 77

Reference Angles

Answer 77

If theta is an angle that lies in a quadrant and if alpha is its reference angle, then sin(theta)=+or-sin(alpha) where the plus or minus sign depends on the quadrant in which theta lies.