Question

How do you find the exact value of `cot ((7pi)/4)`?

Answer 1

On the trig unit circle,

`cot ((7pi)/4) = 1/tan ((7pi)/4)`

`tan ((7pi)/4) = tan (- pi/4 + 2pi)` (same terminal)
`tan (- pi/4 + 2pi) = tan (- pi/4) = - tan (pi/4) = - 1`

`cot ((7pi)/4) = 1/tan = (1/-1) = -1`