Ask Me Help Desk - If sin x = 5 cos x, what is cot x?

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if sin x = 5 cos x, what is cot x?

This is for a trig class that I am completing. Can someone help me solve the eq. Thanks.

What is the definition of cot x?

Remember that:

$cot(x) = \frac{cos(x)}{sin(x)}$

But if you want to solve the equation, why are you looking for cot x? Find tan x.

$sin (x) = 5 cos (x)$

$\frac{sin(x)}{cos(x)} = 5$

$tan(x) = 5$

$\alpha = tan^{-1}(5) = 78.7^o$

So, x = 78.7, 258.7 degrees for 0 < x < 360 degrees

It's easier than that - the problem does not ask to solve for x. If sin(x) = 5 cos(x), then cos(x)/sin(x) = 1/5. Since cos(x)/sin(x) is defined to be cot(x), you have cot(x) = 1/5.

I know, that's why I said the words 'But if' :)

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