DISCUSS: Phases of the Moon During the course of a lunar cycle (about 1 month) the moon undergoes the familiar lunar phases. The phases of the moon are completely analogous to the phases of the sine function described in Exercise 63. The figure below shows some phases of the lunar cycle starting with a “new moon ” “waxing crescent moon ” “first quarter moon” and so on. The next to last phase shown is a “waning crescent moon.” Give similar descriptions for the other phases of the moon shown in the figure. What are some events on the earth that follow a monthly cycle and are in phase with the lunar cycle? What are some events that are out of phase with the lunar cycle?
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Chapter 5 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Blood Pressure The pressure P (in millimeters of mercury) against the walls of the blood vessels of a patient is modeled by P=10020cos8t3 where t is the time (in seconds). (a) Use a graphing utility to graph the model. (b) What is the period of the model? What does it represent in the context of the problem? (c) What is the amplitude of the model? What does it represent in the context of the problem? (d) If one cycle of this model is equivalent to one heartbeat, what is the pulse of the patient? (e) A physician wants the patient’s pulse rate to be 64 beats per minute or less. What should the period be? What should the coefficient of t be?arrow_forward47-54 Equations from a graph The graph of one complete period of a sine or cosine curve is given. a Find the amplitude, period, and horizontal shift. b Write an equation that represents the curve in the form. y=asinkx-b or y=acoskx-barrow_forwardRefraction When you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is 1.333. This is the ratio of the sine of 1 and the sine of 2 (see figure). (a) While standing in water that is 2 feet deep, you look at a rock at angle 1=60 (measured from a line perpendicular to the surface of the water). Find 2. (b) Find the distances x and y. (c) Find the distance d between where the rock is and where it appears to be. (d) What happens to d as you move closer to the rock? Explain.arrow_forward
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