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)
