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

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In summary, The conversation is about a person needing help with calculating the value of x in an equation. Another person suggests using the Cartesian vector method and provides a problem involving a pilot flying from city A to city B. The person in need of help shares their work, and the other person points out a mistake in the last line.
  • #1
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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  • #2
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?)
 
  • #3
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:
  • #4
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:
  • #5
As I see it, the last line is wrong, you divided the LSH by 700 but forgot to divide the RHS by 700. :)
 

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

1. What is the problem asking me to solve?

The problem is asking you to find the value of x that satisfies the equation 246.25 sin x - 676.58 cos x = -27768.42.

2. What is the relationship between sine and cosine functions in this problem?

In this problem, the sine and cosine functions are used together in an equation to solve for x. The sine function represents the vertical component of a right triangle, while the cosine function represents the horizontal component. Together, they can help us find the missing angle (x) in the triangle.

3. How can I solve this equation algebraically?

You can solve this equation algebraically by using trigonometric identities and basic algebraic manipulation. First, try to simplify the equation by factoring out any common factors. Then, use trigonometric identities such as sin^2 x + cos^2 x = 1 to transform the equation into a more manageable form. From there, you can use basic algebraic techniques such as combining like terms and isolating x to solve for its value.

4. Are there any specific values of x that satisfy this equation?

Yes, there are infinite values of x that satisfy this equation. However, we are typically interested in finding the principal value of x, which is the smallest positive angle that satisfies the equation. In this case, the principal value of x is approximately 0.170 radians or 9.73 degrees.

5. Can I use a calculator to solve this problem?

Yes, you can use a calculator to solve this problem. Most scientific calculators have built-in functions for sine and cosine, making it easier to input the equation and solve for x. However, it is important to review the steps and methods used to solve the problem algebraically to better understand the concept behind it.

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