Frequency With simple harmonic motion, the reciprocal of the period is called the frequency. The frequency, given by
Alternating Current In Europe, the voltage of the alternating current coming through an electrical outlet can be modeled by the
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Chapter 4 Solutions
Bundle: Trigonometry, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card
- Refraction 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_forwardBlood 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_forwardMotion of a Projectile If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation (see Figure 10), then the height h of the projectile at time t is given by h=16t2+vtsin Give the equation for h, if v is 600 feet per second and is 45. (Leave your answer in exact value form.)arrow_forward
- Vibrating String When a violin string vibrates, the sound produced results from a combination of standing waves that have evenly placed nodes. The figure (1) illustrates some of the possible standing waves. Lets assume that the string has length . a.For fixed t, the string has the shape of a sine curve y=Asinx. Find the appropriate value of for each of the illustrated standing waves. b.Do you notice a pattern in the values of that you found in part a? What would the next two values of be? Sketch rough graphs of the standing waves associated with these new values of . c.Suppose that for fixed t, each point on the string that is not a node vibrates with frequency 440Hz. Find the value of for which an equation of the form y=Acost would model this motion. d.Combine your answers for parts a and c to find functions of the form y(x,t)=Asinxcost that model each of the standing waves in the figure. Assume that A=1. Figure (1)arrow_forwardShadow length The length s of a shadow cast by a vertical gnomon (a device used to tell time) of height h when the angle of the sun above the horizon is can be modeled by the equation s=hsin90sin 090 (a) Verify that the expression for s is equal to h cot . (b) Use a graphing utility to create a table of the lengths s for different values of . Let h=5 feet. (c) Use your table from part (b) to determine the angle of the sun that results in the minimum length of the shadow. (d) Based on your results from part (c), what time of day do you think it is when the angle of the sun above the horizon is 90?arrow_forwardHeight of a Tower A six-foot person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When the person is 132 feet from the tower and 3 feet from the tip of the shadow, the person’s shadow starts to appear beyond the tower’s shadow. (a) Draw a right triangle that gives a visual representation of the problem. Label the known quantities of the triangle and use a variable to represent the height of the tower. (b) Use a trigonometric function to write an equation involving the unknown quantity. (c) What is the height of the tower?arrow_forward
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