Graph y 120 110 cos 1 2 t . 2

Graph y 4 3 cos x.

Graph y 120 110 cos  1 2 t  . 2

Graph one cycle of y sin  x  2 3

Graph y 4 sin  3x  2 for 0 x 2. x

Graph one cycle of y 2 4 cos  2x  3  .

How does the term affect the graph of y sin  x  ?

How does the term affect the graph of y sin  x  ?

How do you find the period for the graph of y A sin (Bx C)?

How do you find the horizontal translation for the graph of y A sin (Bx C)?

The value k in y k sin x represents a __________ translation. If k is positive, the graph will be shifted k units ________, and if k is negative, the graph will be shifted k units ________.

The value h in y sin (x h) represents a _________ translation. If h is positive, the graph will be shifted h units to the _______, and if h is negative, the graph will be shifted h units to the ________.

The value C in y sin (Bx C) is called the _________.

The graph of y sin (Bx C) will have a horizontal shift of _________.

y 5 sin x

y 2 cos x

y  1 4 cos x 8

y  1 2 sin x G

y 2 sin x

y 4 sin x

y 5 cos x 1

y 1 cos x

y 3 sin x 1

y 6 sin x

y  1 2 cos x 1

y  3 2 cos x G

y 4 4 sin 2x

y 2 2 sin 4x

y 1 cos 3x 20

y 1 sin 3x

y cos (x ) 2

y cos (x ) 2

sin  x  2 3 24.

y sin  x  3 4  G

y sin  x 2

y sin  x

y sin  x 28

y sin  x

y sin  x

y sin  x

y cos  x

y cos  x

y cos  x

y cos  x

y cos   3 x  3

y cos   2 x  2  37

y sin (6x ) 38

y sin (4x )

y 3 sin   1 2 x  6 40

y 2 cos   1 3 x  6  F

y sin (2x ) 42

y sin (2x )

y sin  x 44

y sin  x

cos  2x 46

y cos  2x  4

2 sin x 4

y 3 cos x

y cos  3x

y cos

y 3 sin

y 3 cos

y 1 sin (2x ) 54

y 1 sin (2x ) 5

3 sin  x 56

y 3 sin  x

y 2 cos  2x 58

y 2 cos  2x  G

y 2 3 cos x 60.

y 3 2 sin x  6

y sin (3x ) 62

y cos (3x ) Gr

y 4 cos  2x  , x  6

y sin  3x  , x  65

y 3 cos  x  , 2 x 2 66.

y 2 cos  x  , x

Oscillating Spring A mass attached to a spring oscillates upward and downward. The length L of the spring after t seconds is given by the function L 15 3.5 cos (2t), where L is measured in centimeters (Figure 12). a. Sketch the graph of this function for 0 t 5. b. What is the length the spring when it is at equilibrium? c. What is the length the spring when it is shortest? d. What is the length the spring when it is longest? 6

Oscillating Spring A mass attached to a spring oscillates upward and downward. The length L of the spring after t seconds is given by the function L 8 2 cos (4t), where L is measured in inches (Figure 12). a. Sketch the graph of this function for 0 t 3. b. What is the length the spring when it is at equilibrium? c. What is the length the spring when it is shortest? d. What is the length the spring when it is longest? 1

Sound Wave The oscillations in air pressure representing the sound wave for a musical tone can be modeled by the equation y 0.05 sin (500t 10), where y is the sound pressure in pascals after t seconds. a. Sketch the graph of one complete cycle of the sound wave. b. What is the phase? 7

RLC Circuit The electric current in an RLC circuit can be modeled by the equation y 2 cos (990t 0.64), where y is the current in milliamps after tseconds. a. Sketch the graph of one complete cycle of the current. b. What is the phase?

Arc Length Find the length of arc cut off by a central angle of /6 radians in a circle of radius 10 centimeters.

Arc Length How long is the arc cut off by a central angle of 90 in a circle with radius 22 centimeters?

Radius of a Circle Find the radius of a circle if a central angle of 6 radians cuts off an arc of length 4 feet.

Radius of a Circle In a circle, a central angle of 135 cuts off an arc of length 75 meters. Find the radius of the circle.

Sketch the graph of y 2 cos   2 x  2  . Which of the following matches your graph? a. b. c. d. 3 3 2 1 x y pp 2p 2 p 2 3p 2 1 2 1 2 x y 642 3 2 1 1 2 x y 642 3 2 1 1 2

Identify the vertical translation for the graph of y 1 4 cos  3x  2  . a.  2 b.  2 c. 1 d. 4 77.

Identify the horizontal translation for the graph of y 1 4 cos  3x  2  . a.  2 b.  6 c.  2 d. 1 78. Id

Identify the phase for the graph of y 1 4 cos  3x  2  . a.  2 b.  6 c.  2 d. 1 SECTIO