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

Yes, and the light will be effective on the opposite wall for the same amount of time.In summary, the searchlight is rotating from a point 50m from the prison walls and its rotation is represented by the equation d=50sec(2πt). To graph the path of light for 2 minutes, you can plot d=sec(2πt) on a coordinate system with d vs t and then transform it into d=sec(2πt). When the effective distance for the light is 100m, the prison wall will not be illuminated sufficiently for the same time it takes the light to travel that distance, and it will take the same amount of time for the light to become effective on
  • #1
crosbykins
53
0

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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  • #2
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.
 

1. How do I approach a trig function word problem?

To solve a trig function word problem, start by reading the problem carefully and identifying the given information and what you are trying to solve for. Then, use the appropriate trigonometric function (sine, cosine, or tangent) to set up an equation and solve for the missing variable.

2. What is the purpose of using trigonometric functions in word problems?

Trigonometric functions allow us to calculate missing sides or angles in a right triangle, which is often needed in real-life situations such as navigation, engineering, and physics.

3. How do I know which trigonometric function to use?

The trigonometric function used depends on the given information and what you are trying to solve for. Remember SOH-CAH-TOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

4. Can I use a calculator to solve trig function word problems?

Yes, you can use a calculator to find the values of trigonometric functions. However, it is important to understand the concept and steps involved in solving the problem manually.

5. What are some tips for solving trig function word problems?

Some tips for solving trig function word problems include drawing a diagram, labeling the sides and angles, and using trigonometric ratios to set up an equation. It is also helpful to understand the relationships between the sides and angles in a right triangle.

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