On a day when the sun passes directly overhead at noon, a 6-ft-tall man casts a shadow of length6|tan(t)|S(t) =where S is measured feet and it is the number of hours since 6 A.M.8:00 A.M.(a) Find the length of the shadow at 8:00 A.M., noon, and 2:00 P.M. (Round your answers to two decimal places.)2:00 P.M.-5Sft0⁰noon6 ftft(b) Sketch a graph of the function S for 0 < t < 12.00O t = 3 and t =9; that is, at 9:00 A.M. and 3:00 P.MO t = 3 and t = 9; that is, at 3:00 A.M. and 9:00 P.MOt= 6; that is, at noonO t = 1 and t = 11; that is, at 7:00 A.M. and 5:00 P.M0⁰J6(c) From the graph, determine the values of t at which the length of the shadow equals the man's height. To what time of day does each of these values correspond?O t = 1 and t = 11; that is, at 11:00 A.M. and 1:00 P.M(d) Explain what happens to the shadow as the time approaches 6 P.M. (that is, as t→→ 12").O The shadow gets increasingly shorter.O The length of the shadow approaches feet.O The shadow gets increasingly longer.O The length of the shadow approaches 12 feet.O The length of the shadow approaches 92 feet.12

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On a day when the sun passes directly overhead at noon, a 6-ft-tall man casts a shadow of length 6 - |tan(+4)| where S is measured in feet and t is the number of hours since 6 A.M. S(t) = (a) Find the length of the shadow at 8:00 A.M., noon, and 2:00 P.M. (Round your answers to two decimal places.) 8:00 A.M. ft S noon S ft 6 ft (b) Sketch a graph of the function S for 0 < t < 12. 2:00 P.M. NU 5 6 ft S MNM 5 12 t 12 12 (c) From the graph, determine the values of t at which the length of the shadow equals the man's height. To what time of day does each of these values cor O t = 1 and t = 11; that is, at 11:00 A.M. and 1:00 P.M O t = 3 and t = 9; that is, at 9:00 A.M. and 3:00 P.M O t = 3 and t = 9; that is, at 3:00 A.M. and 9:00 P.M O t = 6; that is, at noon O t = 1 and t = 11; that is, at 7:00 A.M. and 5:00 P.M

On a day when the sun passes directly overhead at noon, a 6-ft-tall man casts a shadow of length 6 - |tan(+4)| where S is measured in feet and t is the number of hours since 6 A.M. S(t) = (a) Find the length of the shadow at 8:00 A.M., noon, and 2:00 P.M. (Round your answers to two decimal places.) 8:00 A.M. ft S noon S ft 6 ft (b) Sketch a graph of the function S for 0 < t < 12. 2:00 P.M. NU 5 6 ft S MNM 5 12 t 12 12 (c) From the graph, determine the values of t at which the length of the shadow equals the man's height. To what time of day does each of these values cor O t = 1 and t = 11; that is, at 11:00 A.M. and 1:00 P.M O t = 3 and t = 9; that is, at 9:00 A.M. and 3:00 P.M O t = 3 and t = 9; that is, at 3:00 A.M. and 9:00 P.M O t = 6; that is, at noon O t = 1 and t = 11; that is, at 7:00 A.M. and 5:00 P.M

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 67E

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