Question

find θ if cotθ= -.577

Answer 1

\[\cot \theta = \frac{1}{\tan \theta} \rightarrow \tan \theta = \frac{1}{\cot \theta}\]
\[\theta = \tan^{-1} (\frac{1}{-.577})\]
use scientific calculator

Answer 2

well cot = 1/tan

so then if

\[\cot(\theta) = -0.577\]

take the reciprocal of each and

\[\tan(\theta) = \frac{1}{-0.577}\]

and tan is negative in the 2nd quadrant and 4th quadrant

so find

\[\tan (\theta) = \frac{1}{0.577}\]

then use

2nd quadrant

\[ Angle = 180 - \theta\]

4th quadrant

\[Angle = 360 - \theta\]

hope it makes sense