Question

How do you find the exact value for csc (7pi/6) and cot (-pi/3)

Answer 1

\(\Large\bf \color{#008353}{\text{Welcome to OpenStudy! :)}}\)

Answer 2

\[\Large\bf\sf \cot(-\pi/3)\quad=\quad \frac{1}{\tan(-\pi/3)}\]Do you know how to find tan(-pi/3)?

Answer 3

Csc= 1/sin

Answer 4

use the Unit Circle :)

Answer 5

Tangent is an `odd` function,
So this holds true,\[\Large\bf\sf \tan(-\theta)\quad=\quad -\tan(\theta)\]
So we can further simplify it to,\[\Large\bf\sf \cot(-\pi/3)\quad=\quad \frac{1}{\tan(-\pi/3)}\quad=\quad \frac{1}{-\tan(\pi/3)}\]And then yah, use your unit circle from there :o

Answer 6

would csc's final answer be -2?

Answer 7

Yup

Answer 8

and would cot's answer be \[\sqrt{3}\]?

Answer 9

\(\bf tan(\theta)=\cfrac{{\color{red}{ \square }}}{{\color{blue}{ \square }}}\qquad cot(\theta)=\cfrac{{\color{blue}{ \square }}}{{\color{red}{ \square }}}
\\ \quad \\ \quad \\

tan\left(\cfrac{-\pi}{3}\right)=\cfrac{{\color{red}{ \square }}}{{\color{blue}{ \square }}}\qquad cot\left(\cfrac{-\pi}{3}\right)=?\)