Question

how to solve arctan[tan(7pi /4)]

Answer 1

7pi/4

Answer 2

atan and tan are inverse functions

Answer 3

but why tan (7pi/4) =-1

Answer 4

so you can simplify 7pi/4 and write that 7pi/4=-pi/4 or 3pi/4

Answer 5

yes tan and arctan are inverse of each other

Answer 6

so the answer will change ?!!

Answer 7

no, it will still be -pi/4

Answer 8

find a place on the unit circle in the interval
\[[-\frac{\pi}{2},\frac{\pi}{2}]\]
where the tangent is also -1

Answer 9

\[\tan(\frac{7\pi}{4})=\frac{\sin(\frac{7\pi}{4})}{\cos(\frac{7\pi}{4})}=-1\]