Cos(x)+sin(x) = 0, Find all values?

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The equation cos(x) + sin(x) = 0 has a primary solution at x = 3π/4. Additional solutions can be found by adding integer multiples of π to this value, resulting in an infinite set of solutions. The confusion arises from a calculator error when evaluating cos(7π/4) + sin(7π/4), which yields a value close to zero but not exactly zero. This discrepancy is attributed to the limitations of the calculator's precision. The initial approach to finding the solutions is correct, and the calculator's output does not invalidate the solution.
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Homework Statement


Cos(x)+sin(x) = 0, Find all values?



Homework Equations





The Attempt at a Solution


I've found the first solution, which is 3pi/4 and I figured I can just add pi to that value over and over to obtain the infinite other values. But when I punch it in my calculator it's coming up that cos(7pi/4)+sin(7pi/4) = 0.000000000021

I'm not sure if this is a calculator computation issue or I'm doing something wrong.. Thanks for any help.
 
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DrummingAtom said:

Homework Statement


Cos(x)+sin(x) = 0, Find all values?



Homework Equations





The Attempt at a Solution


I've found the first solution, which is 3pi/4 and I figured I can just add pi to that value over and over to obtain the infinite other values. But when I punch it in my calculator it's coming up that cos(7pi/4)+sin(7pi/4) = 0.000000000021

I'm not sure if this is a calculator computation issue or I'm doing something wrong.. Thanks for any help.
No, you're not doing anything wrong. This error is due to the calculator.
 

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