Help Solving for x: 246.25 sin x - 676.58 cos x = -27768.42

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Discussion Overview

The discussion revolves around solving the equation 246.25 sin x - 676.58 cos x = -27768.42, which is part of a larger problem involving a pilot's navigation from city A to city B, factoring in wind conditions. The scope includes mathematical reasoning and application of vector methods in a real-world context.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • James seeks assistance in calculating the value of x from the given equation.
  • One participant suggests considering the minimum and maximum values of sin x and cos x to evaluate the expression's limits.
  • Another participant expresses doubt about the solvability of the equation, indicating a potential mistake in its derivation.
  • A participant clarifies that the problem is derived from a navigation scenario involving a pilot, specifying the need to use Cartesian vector methods.
  • James shares his work related to the problem, providing links to images for further examination.
  • Another participant points out a possible error in James's calculations regarding the division of terms in the equation.

Areas of Agreement / Disagreement

Participants express uncertainty about the solvability of the original equation and identify potential errors in the calculations presented. There is no consensus on the correct approach or solution at this stage.

Contextual Notes

The discussion highlights limitations in the initial equation's context and the need for specific methods (Cartesian vector) to solve the navigation problem. There are unresolved mathematical steps and assumptions regarding the derivation of the equation.

Who May Find This Useful

This discussion may be useful for students or individuals interested in vector methods, navigation problems, and trigonometric equations in applied contexts.

James_fl
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Hello, could anyone help me calculate the value of x?

246.25 sin x - 676.58 cos x = -27768.42

Thank you..

James
 
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You know the smallest value sin x can have, and the largest value cos x can have. So what is the smallest value 246.25 sin x - 676.58 cos x can have?


(Or are you expected to work with complex numbers?)
 
Ah, yea that's right. it's impossible to solve it.

Well, this equation is derived from somewhere else, and I might have done mistake in doing it.

This is the question:

Use Cartesian vector method to solve the problem. If you use any other method, you will receive zero.

A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 70 degree. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110 degree. What heading should the pilot take to reach his or her destination? How long will the trip take?

Could you help me with this please? I will post my work in 5 minutes.
 
Last edited:
OK, here is my work:

http://i66.photobucket.com/albums/h242/jferdina/Bearing.jpg"
http://i66.photobucket.com/albums/h242/jferdina/Bearing-continued.jpg"
 
Last edited by a moderator:
As I see it, the last line is wrong, you divided the LSH by 700 but forgot to divide the RHS by 700. :)
 

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