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Pre-Calculus Solving Problems With Trigonometry

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Using Angle of Depression The angle of depression of a buoy from the top of the Barnegat Bay lighthouse 130 ft above the surface of the water is 6°. Find the distance x from the base of the light house to the buoy.

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Making Indirect Measurements The world’s tallest smokestack at the International Nickel Co., Sudbury Ontario, casts a shadow that is approx. 1580 ft long when the sun’s angle of elevation (measured from the horizon) is 38°. How tall is the smokestack?

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Finding Height Above Ground A large helium-filled penguin is moored at the beginning of a parade route awaiting the start of the parade. Two cables attached to the underside of the penguin make angles of 48° and 40° with the ground and are in the same plane as a perpendicular line from the penguin to the ground. If the cables are attached to the ground 10 feet from each other, how high above the ground is the penguin?

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Using trigonometry In Navigation A U.S. Coast Guard patrol boat leaves Port Cleveland and averages 35 knots traveling for 2 hours on a course of 53° and then 3 hours on a course of 143°. What is the boat’s bearing and distance from Port Cleveland?

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Simple Harmonic Motion A point moving on a number line is in simple harmonic motion if its directed distance d from the origin is given by either d = a sin(wt) or d = a cos (wt), where a and w are real numbers and w>0. The motion has frequency w/2π, which is the number of oscillations per unit of time.

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Calculating Harmonic Motion A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 5 cm, find the modeling equation if it takes 2 seconds to complete one cycle.

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Calculating Harmonic Motion In a mechanical linkage, a wheel with an 8-cm radius turns with an angular velocity of 8∏ radians/sec. (a) What is the frequency of the piston? (b) What is the distance from the starting position (t=0) exactly 3.45 seconds after starting?

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Problems to Try Page 337-342 1-9 odd, 17, 21, 27, 33, 51, 53, 55

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