Question

How do you find the value of cot 14pi/3
Find the Value using Unit Circle

Answer 1

you'll notice from the unit circle that the values of cot repeat on a cycle every pi/2 radians.

this is because it is a periodic function with a period of pi/2. Looking at a graph of cotan, by googling it, might help visualize.

So:

\[\cot (x) = \cot(x \pm k\frac{ \pi }{ 2 })\]Where k is any integerSo:\[\cot(\frac{ 14 \pi }{ 3 }) = \cot( \frac{ 14\pi }{ 3 } \pm k \frac{ \pi }{ 2 })\]

keep plugging in k values (1,2,3,4, ect..) until you fall between 0 and 2 pi and you can use the value using the unit circle

Answer 2

I understand 14pi/3 is 840 Degrees but I need the answer in radians. I can do the trig functions with sin cos and tan, but csc sec and cot is where I am not understanding what to do. Cot = 1/tan so does that mean 1/ 14pi/3?

Answer 3

no. 1/tan(14pi/3) = cot(14pi/3)

Answer 4

you can also use cot(x) = cos(x)/sin(x)

Answer 5

tab 14pi/3 = -\[\sqrt{3}\] so does that mean cot 14pi/3 = - 1 / \[\sqrt{3}\]

Answer 6

yes

Answer 7

How do you your answer when you get something such as \[2\sqrt{3}\div3\]

Answer 8

when you have to put it over 1

Answer 9

you can't really simplify it.

I'd present it as:

\[\frac{ 2\sqrt3 }{ 3 }\]
unless you mean, to submit to an online quiz or whatever

Answer 10

Takehome quiz, but another question Division by 0 is undefined correct?

Answer 11

correct

Answer 12

Thanks for your help!