630 CHAPTER 6 The Circular Functions and Their Graphs Connecting Graphs with Equations Determine an equation of the form y = acos bx or y = asin bx, where b 70, for the given graph. See Example 6. 41. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 44. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 42. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 45. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 43. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 46. x y –1 –2 –3 1 2 3 2p p 0 3p 2 p 2 (Modeling) Solve each problem. 47. Average Annual Temperature Scientists believe that the average annual temperature in a given location is periodic. The average temperature at a given place during a given season fluctuates as time goes on, from colder to warmer, and back to colder. The graph shows an idealized description of the temperature (in °F) for approximately the last 150 thousand years of a particular location. Years ago Average Annual Temperature (Idealized) 150,000 100,000 50,000 80° 65° °F 50° (a) Find the highest and lowest temperatures recorded. (b) Use these two numbers to find the amplitude. (c) Find the period of the function. (d) What is the trend of the temperature now? 48. Blood Pressure Variation The graph gives the variation in blood pressure for a typical person. Systolic and diastolic pressures are the upper and lower limits of the periodic changes in pressure that produce the pulse. The length of time between peaks is the period of the pulse. (a) Find the systolic and diastolic pressures. (b) Find the amplitude of the graph. (c) Find the pulse rate (the number of pulse beats in 1 min) for this person. Time (in seconds) Blood Pressure Variation Pressure (in mm mercury) 0.8 1.6 Systolic pressure Diastolic pressure 80 40 0 120 Period = 0.8 sec
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