Suppose I have a angle X=100 and angle Y=60.
when we add X 15 times it gives Y.
How do I calculate that?
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Heisenberg
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Hint: You want to solve $100x\equiv 60\pmod{360}$. We are using the fact that two angles are coterminal if they differ by an integer multiple of $360^\circ$.
Equivalently (divide through by $20$) you want to solve $5x\equiv 3\pmod{18}$.
André Nicolas
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Does that mean I need to get modular multiplicative inverse of 60,360? – Heisenberg Mar 15 '14 at 17:55
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Multiplicative inverse doesn't work for $ax\equiv b\pmod{m}$ if $a$ and $m$ are not relatively prime. That's why I divided through by $20$, the gcd of $100$ and $360$. Once we are at $5x\equiv 3\pmod{18}$, we can multiply through by the inverse of $5$ modulo $18$ to find $x$. Or else, since $18$ is a pretty small number, we can find $x$ by "trial and error." – André Nicolas Mar 15 '14 at 17:59