Trig+geometry. need help finding the angle

[deepak]

\(\displaystyle \tan\left(\phi_2\right)\, =\, \dfrac{1\, \mbox{m}}{1\, \mbox{m}}\)

\(\displaystyle \phi_2\, =\, \tan^{-1}(1)\, +\, 90^{\circ}\)

. ..\(\displaystyle \, =\, 45^{\circ} + 90^{\circ}\)

. ..\(\displaystyle \, =\, 135^{\circ}\)

Can you explain why we add 90 ?

 

[Ishuda]

\(\displaystyle \tan\left(\phi_2\right)\, =\, \dfrac{1\, \mbox{m}}{1\, \mbox{m}}\)

\(\displaystyle \phi_2\, =\, \tan^{-1}(1)\, +\, 90^{\circ}\)

. ..\(\displaystyle \, =\, 45^{\circ} + 90^{\circ}\)

. ..\(\displaystyle \, =\, 135^{\circ}\)

Can you explain why we add 90 ?

Actually adding 90\(\displaystyle ^{\circ}\, [=\,\frac{\pi}{2}]\) is incorrect unless there is something you neglected to tell us. Note that
tan(x \(\displaystyle \pm\, \frac{\pi}2\)) = - cot(x)

However, since the tangent has a period of \(\displaystyle \pi\), you could have added or (subtracted) 180\(\displaystyle ^{\circ}\).