Question

Evaluate cot(-405°) I need help please

Answer 1

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

$cot (\theta) = \frac{1}{tan(\theta)}$

Answer 2

Answer:

-1

Step-by-step explanation:

It always happens that:

$\cos \theta = \frac{1}{\tan \theta}$

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)