Non Permissible values of cot ⁡ ( x )Why is it that the non-permissible values...

dream13rxs

dream13rxs

Answered

2022-07-05

Non Permissible values of cot ( x )
Why is it that the non-permissible values of cotangent x is only where sin ( x ) = 0 and not also where cos ( x ) = 0

Answer & Explanation

Nicolas Calhoun

Nicolas Calhoun

Expert

2022-07-06Added 15 answers

one way you can see this is that
cot x = 1 tan x = 1 sin x cos x = cos x sin x
which is 0 when cos x = 0, and undefined when sin x = 0
Lillianna Andersen

Lillianna Andersen

Expert

2022-07-07Added 3 answers

The tangent of x is defined as the the sine of x divided by the cosine of x, so
tan x = sin x cos x
If x=0 then product is 0/1=0, which is a real solution.
However for
cot x = cos x sin x
Now, if x=0, then the product is 1/0 which is undefined, meaning that a solution does not exist, which means that sinx cannot be equal to 0 for cotx to exist

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