Quod Erat Demonstrandum

2008/01/09

[CE][AM] 錯在哪裡 – general solutions to trigonometric equations

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 12:01 下午

Given that $a,b$ are non-zero constants such that $|a| < 1$ and $|b| < 1$.

Solve the following simultaneous equations

$\sin(x) = a$ – – – (1)
$\cos(x) = b$ – – – (2)

Solution (so-called)

divide (1) by (2), yield

$\tan(x) = \frac{a}{b}$

Hence

$x = 180^{o}n + \tan^{-1}(\frac{a}{b})$ where $n$ is any integer