Urgent help needed: trig function word problem! (, thanks in advance!)

  • Thread starter crosbykins
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  • #1
crosbykins
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Homework Statement



A searchlight is rotating from a point 'P' positioned 50m from the prison walls. The rotation of the light is represented by the equation d = 50sec2pi(t), where d is the distance in meters, from the light to the wall, and 't' is time in minutes.

a) graph the the path of light for 2 min
b) If the effective distance for the light is 100m, how many seconds elapse before the prison wall is not illuminated sufficiently?
c)How many seconds does it take for the light to become effective on the opposite wall?



Homework Equations


***Diagram is attached


The Attempt at a Solution



-i don't get how to graph this
-would it be correct to enter y = 50x/cos 2 pi in my graphing calculator?

b) so would you just do
100 = 50sec 2pi t

and solve for t

c) 50 = 50 sec 2pi t
and solve for t
 

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Answers and Replies

  • #2
Mentallic
Homework Helper
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The equation is actually [tex]d=50sec(2\pi t)[/tex] and not [tex]d=50sec(2\pi)t=50t[/tex] since [itex]cos(2\pi)=1[/tex]

a) Well it's asking you the same question as if it were to ask you to graph y=cos(x), just draw up a coordinate system with d vs t, rather than y vs x and first start with drawing up d=sec(t), then transform this graph into d=sec(2[itex]\pi[/itex]t) etc.

b) I'm not quite sure of this one because I don't know where the search light starts from, but you will know how to solve it by just simultaneously solving the search light equation and the equation d=100. It will give you the value(s) of t when d=100.
 

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