How do you find: cot(-5pie/4)?

you have to know that cotx = 1/tanx

so you could just trustfully change your calculator to radians
enter 5*pi/4, press =, press +/-,
then press Tan, =, then the 1/x key
you should get -1

or...

you could do it the more rewarding way without a calculator.

pi/4 radians is 45º, so 5pi/4 is 225º
-225º is a clockwise rotation and lands you in the second quadrant where the tan is negative, and 45º up from the x-axis.
now tan45º=1, so tan(-225º)=-1
then cot(-225)=1/-1=-1

thanks.