Question

what is the correct definition for cot theta?

Answer 1

answer choices

Answer 2

Technically \[
\cot (\theta) = \tan(\pi/2-\theta)
\]Or in general: \[
\text{co}\color{red}{\text{fun}}(\theta) = \color{red}{\text{fun}}(\pi/2-\theta)
\]

Answer 3

Since \[
\tan(\theta) = \frac{\sin(\theta)}{\text{cosin}(\theta)}
\]We could say \[
\text{cotan}(\theta) = \frac{\text{cosin}(\theta)}{\text{cocosin}(\theta)}
\]Two \(\text{co}\)s cancel out since \(\pi/2-(\pi/2-x) = x\)

Answer 4

So \[
\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}
\]

Answer 5

thank you so much! I understand

Answer 6

i always thought cot(x) = 1/tan(x) but that turned out to be false because 1/tan(x) isn't the same as cos(x)/tan(x)

Answer 7

typo *cos(x)/sin(x)*

Answer 8

Uhhh. \(\cot\theta = 1/\tan\theta\)

Answer 9

But \[
[\tan\theta]^{-1}\neq \tan^{-1}\theta
\]

Answer 10

I think there is a struggle between the two definition of cot(x) and tan(x).

cot(x) = cos(x)/sin(x), with sin(x) ≠ 0

tan(x) = sin(x)/cos(x), with cos(x) ≠ 0

but 1/tan(x) = 1/( sin(x)/cos(x)) with both sin(x),cos(x) ≠ 0.

Now I don't what the convention is. If I graph 1/tan(x) in my calculator, then it's undefined at x = pi/2. But wolfram somehow just make cot(x) = 1/tan(x)