What is the value of arctan(tan(pi)) ?

The value of arctan(tan(pi)) is 0

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arctan(tan(pi))

arctan (tan (π))

0

Solution steps

arctan (tan (π))

Use the following trivial identity:

tan (π) = 0

tan (π)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= arctan (0)

= arctan (0)

Use the following trivial identity:

arctan (0) = 0

arctan (0)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= 0

= 0

tan (- 0.5)

sec (\frac{15 π}{4})

20 cos (4 0^{\circ})

cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

cot (\frac{17 π}{6})