System Of Trigonometric Equations

In summary, to solve the system of trigonometric equations in MATLAB, you need to put the sin x and cos x terms on one side and the rest on the other side, square both equations and add them, and solve for x and y using simultaneous equations in cos x and sin x.
  • #1
nradam
9
0
Code:
a*sin(x)=b*sin(th)+c*sin(y)
d+a*cos(x)=b*cos(th)+c*cos(y)

Find x and y if all others are constants. I don't get how to solve this system of trigonometric equations in matlab. Please help me out friends.

Thanks in advance.
 
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  • #2
Put the sin x and cos x terms on one side and the rest on the other side.
Square both equations and add them.

You get something like

a^2 + c^2 + 2ac cos(x-y) = b^2 + d^2 - 2bd cos th

Solve that for x-y, which gives you y = x + k for some value of k.

Then you can turn the original equations into simultaneous equations in cos x and sin x
 

1. What is a system of trigonometric equations?

A system of trigonometric equations is a set of two or more equations that involve trigonometric functions, such as sine, cosine, and tangent, and their respective variables. The goal is to find values for the variables that satisfy all of the equations simultaneously.

2. How are trigonometric equations solved?

Trigonometric equations can be solved using various methods, such as algebraic manipulation, substitution, or graphing. The most common approach is to use trigonometric identities to simplify the equations and then solve for the variables.

3. What are some real-world applications of trigonometric equations?

Trigonometric equations are used in many fields, including engineering, physics, astronomy, and navigation. They can be used to calculate distances, angles, and heights, as well as to model periodic phenomena such as sound or light waves.

4. Can a system of trigonometric equations have multiple solutions?

Yes, a system of trigonometric equations can have multiple solutions. This can occur when the equations overlap or intersect at multiple points. It is important to check all possible solutions to ensure that they satisfy all of the equations in the system.

5. What are some common challenges when solving trigonometric equations?

Some common challenges when solving trigonometric equations include identifying which trigonometric identities or properties to use, dealing with multiple solutions, and working with complex or nested expressions. It is also important to carefully check solutions to ensure they are valid for all of the equations in the system.

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