Given \(\displaystyle{\sin{{\left({10}^{{{100}}}\right)}}}+{\sin{{\left({n}\right)}}}={0}\) find n.

tambustqaze

tambustqaze

Answered question

2022-03-25

Given
sin(10100)+sin(n)=0
find n.

Answer & Explanation

shvatismop1rj

shvatismop1rj

Beginner2022-03-26Added 10 answers

And regarding your problem, considering n in degrees, you want to know why we have,
10100280 (mod 360)
Right? Well, you can simply verify the result using Euler's Totient Theorem.
ϕ(360)=ϕ(32×23×5)
=360(112)(113)(115)=96
where ϕ(n) is the Euler Totient function that counts the totatives of n.
Now, what the theorem tells us is,
10961 (mod 360)10100104(mod 360)
104=1000×10(80)×100(8)×1000
(8)×(80)640280 (mod 360)

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