Question

Evaluate cot(-405°) I need help please

Answer 1

`x^\circ = x^\circ +360n`
where n is a whole number


`cot (\theta) = (1)/(tan(\theta))`

Answer 2

-1

Explanation:

It always happens that:

`\cos \theta = (1)/(\tan \theta)`

So, we will find
`\tan (-405)`. In order to do that, remember that
`\tan \theta = \tan \theta + 180`. Then

`\tan(-405) = \tan(-405 + 180) =\tan(-225)`

We repeat that until we have a positive number in the argument.

`\tan(-225) = \tan(-225 + 180) =\tan(-45)`

`\tan(-45) = \tan(-45 + 180) =\tan(135)`

As we can see, we have to find
`\tan(135)`. If we draw an angle of 135, we can see in the image that the abscissa is negative (because is in the left), and the ordinate is positive. Then

`\tan(135) = -\tan(45) = -1.`

Finally

`\tan(-405) = -1.`

(tan(45) is a known value. Also the tan(30) and tan(60). You can usually go from there)