Graphing Sine and Cosine Graphing csc, sec, tan, and cot Writing Equations Modeling with Trig. Functions

Row 1, Col 1 y = 4sin2x

1,2 y = tanx

1,3 y = 3cosx or y = -3sin(x – π/2) or y = 3sin(x – 3π/2)

1,4 The voltage of an alternating current can be modeled by the function V = AsinBt, where t is measured in seconds. If the voltage alternates between -180 and 180 volts, and the period is 70 seconds, find V as a function of t. Assume the voltage begins at 0 and increases at first. V = 180sin[(π/35)t]

2,1 y = cos4x

2,2 y = 3cscx

2,3 y = sin3x or y = cos3(x – π/6)

2,4 The diameter of a Ferris wheel is 165 feet. It rotates once every ¾ minute, and the bottom of the Ferris wheel is 9 feet above the ground. Find an equation that gives the passenger’s height above the ground at any time (in minutes)during the ride. Assume the passenger starts the ride at the bottom of the wheel. y = cos[(8π/3)x] or y = cos [(8π/3)(x – 3/8)]

3,1 y = 1 + 3cos[(π/3)(x – 1)]

3,2 y = -2sec(0.5x)

3,3 y = 2cos3x or y = -2cos3(x - π/3) or y = -2sin3(x- π/6)

3,4 A mass attached to a spring moves upward and downward periodically. The length, L, of the string after t seconds is given by the function L = 15 – 3.5cos(2πt) where L is measured in centimeters. Find the average, longest, and shortest lengths of the spring. Average= 15cm ; Longest = 18.5cm; Shortest=11.5cm

4,1 y = 4cos[2x – (π/2)]

4,2 y = 2cot[x – (π/4)]

4,3 y = 2 – 4sin(πx) or y = 2 + 4cosπ(x – 1.5) or y = 2 - 4cosπ(x – 0.5)

4,4 The diameter of a car's tire is 52 cm. While the car is being driven, the tire picks up a nail. The height of the nail above the ground in terms of the distance the car has traveled since the tire picked up the nail can be modeled by a sinusoidal function. Write an equation to model the height of the nail at any given distance. When the car has traveled 2 meters, what will the height of the nail be? y = 26 – 26cos(x/26) ; height = 21.8 cm

5,1 y = 1.5 – 0.5sin(3x + π)

5,2 y = 2 + csc[ 3x – (π/2)]

5,3 y = 3cos2[x + (3π/8)] or y= -3sin2[x + (π/8)] or y = -3cos2[x - (π/8)] or y= 3sin2[x - (3π/8)]

5,4 Iguanas are cold-blooded or ectothermic organisms with their body temperature depending on the external temperature. Their natural habitat lies near the equator, where the sun shines about 12 hours a day. The iguana's temperature cycles during the day, with a low of 75°F at about 3 am and a high of 104°F at about 3 pm. Assume that the body temperature of an iguana can be modeled using the following function: y = k + A sin(B(x - h));where x is in hours from midnight. a.Use the data above write an equation, then sketch a graph for the temperature of a typical iguana for one day (starting at midnight). b. A temperature of 88°F for at least 12 hours a day is critical for the health of an iguana. About how many hours a day does your iguana model give this temperature? (Use the graph which you have created to make a reasonable estimate.) Write a time interval for when the iguana’s temperature is above 88°F y = sin[(π/12)(x – 9)] ; 12 hrs; 9 ≤ x ≤ 21