How do you evaluate cot^-1(-5)?

1 Answer
Dec 12, 2015

348.69^@ or 168.69^@

Explanation:

theta=cot^-1(-5)
cottheta=-5
1/tantheta=-5
tantheta=-1/5
theta=tan^-1(-1/5)
theta~~-11.31^@(348.69^@)

However, according to the CAST rule, cottheta and tantheta are also negative in second quadrant.

To find the second possible angle, find the related acute angle, and subtract the value from 180^@.

Finding the related acute angle:
360^@-348.69^@
=11.31^@

Finding the second possible angle:
180^@-11.31^@
=168.69^@

:., the possible angles are approximately 348.69^@ and 168.69^@.