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

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The discussion revolves around solving the equation 246.25 sin x - 676.58 cos x = -27768.42, with participants noting the limitations of sine and cosine values. It is highlighted that the equation may not be solvable as presented, and there is a suggestion that it could stem from an error in derivation. The main focus shifts to a related problem involving a pilot's navigation, requiring the use of Cartesian vector methods to determine the correct heading and travel time. A participant shares their work on the problem, but another points out a mistake in their calculations regarding the division by the plane's speed. The conversation emphasizes the need for accurate mathematical methods in solving vector-related problems.
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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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