I am resolving some trigonometric equation systems. A typical system (the following one is invented) could be:
$\sin(x) + \cos(y) = 1.5$
$2\sin(x) + 3\cos(y) = 1$
After getting the values, you just go to the unit circle and find the trigonometric solution.
However, I stumbled upon a different equation system (again invented system, I am not interested in the solution itself):
$\cot(x) + \cot(y) = 2$
$2\cot(x) + 3\cot(y) = 3.2$
Which I do not know how to proceed, since I cannot compare to the typical values found in the unit circle (sin/cos). What should I proceed after obtaining the values for $x [\cot(x)]$ and $y [\cot(y)]$$?
$\endgroup$2 Answers
$\begingroup$From what you've written:
$-2cot(x)-2cot(y)=-4$
$2cot(x) + 3cot(y) = 3.2$
Therefore, $cot(y)=-0.8$ and $cot(x)=2.8$. You can then write $x$ and $y$ as inverse of these values. Does this answer your question?
Recall that we can calculate $\cot\theta$ using $\sin\theta$ and $ \cos\theta$ for any angle $\theta$:
$$\cot \theta = \dfrac{\cos \theta}{\sin \theta}$$
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