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athrun200
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Homework Statement
Q4(b)
http://www.physics.hku.hk/~phys1315/doc/MPI_HW3.pdf"
Homework Equations
The Attempt at a Solution
After I set fx and fy =0
I get cosx=cosy.
How to solve it?
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I don't understand this statement...HallsofIvy said:If cos(x)= cos(y) then sin(x)=±sin(y)
Sorry that I didn't notice your reply.lanedance said:Now going back to the main requirement for fx=fy=0:
cos(x)=-cos(x+y)
cos(y)=-cos(x+y)
can you do a similar process to find allowable (x,y) pairs?
To solve for x and y in cosx=cosy, you can use the inverse cosine function (cos-1). First, rewrite the equation as cosx-cosy=0. Then, use the identity cosx-cosy=2sin((x+y)/2)sin((x-y)/2) to get sin((x+y)/2)sin((x-y)/2)=0. Finally, set each factor equal to 0 and solve for x and y.
When solving for x and y in cosx=cosy, the process is the same. The only difference is the values you plug in for x and y in the inverse cosine function. For example, if you are solving for x, you would use cos-1(cosy). If you are solving for y, you would use cos-1(cosx).
Yes, you can use a calculator to solve cosx=cosy. Most scientific calculators have an inverse cosine function (cos-1) which you can use to find the values of x and y.
Yes, there are a few special cases when solving for x and y in cosx=cosy. These include when x and y are equal, when x and y are opposite (i.e. differ by 180 degrees), and when x and y are complementary (i.e. add up to 90 degrees). In these cases, the values of x and y will be the same or differ by a multiple of 360 degrees.
You can check your solution for x and y in cosx=cosy by plugging the values back into the original equation. If the equation still holds true, then your solution is correct. Additionally, you can also graph the equation and see if the points where the graphs intersect match with your solution for x and y.