Is -arctan(x/y) equal to arctan(y/x)?

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SUMMARY

The expressions -arctan(x/y) and arctan(y/x) are not equivalent. This conclusion is supported by testing specific values, such as x=1 and y=1, which demonstrate the discrepancy between the two functions. However, it is noted that the derivatives of these two expressions, with respect to x while keeping y constant, are equivalent. This insight may assist in understanding their relationship in calculus contexts.

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Homework Statement


-arctan(x/y) = arctan(y/x) ?

Are they equivalent? I can't find anything online and I have seen that my solution to some problem involves
-arctan(x/y) and it agrees with Wolfram Alpha. On the other hand, my professor's solution shows the arctan(y/x) and this is why I am doubtful.

Any ideas?
Thank you.
 
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knowLittle said:

Homework Statement


-arctan(x/y) = arctan(y/x) ?

Are they equivalent? I can't find anything online and I have seen that my solution to some problem involves
-arctan(x/y) and it agrees with Wolfram Alpha. On the other hand, my professor's solution shows the arctan(y/x) and this is why I am doubtful.

Any ideas?
Thank you.

They aren't equal. That would be silly, put x=1 and y=1. But the derivative d/dx with y a constant of arctan(y/x) is the same as the derivative of -arctan(x/y) if that's any help.
 
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