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 property:

tan (- x) = - tan (x)

tan (- π) = - tan (π)

= arctan (- tan (π))

Use the following property:

arctan (- x) = - arctan (x)

arctan (- tan (π)) = - arctan (tan (π))

= - arctan (tan (π))

tan (π) = tan (0)

tan (π)

Rewrite

π

π + 0

= tan (π + 0)

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + 0) = tan (0)

= tan (0)

= - arctan (tan (0))

Rewrite using trig identities:

arctan (tan (0)) = 0

arctan (tan (0))

Use the following trivial identity:

tan (0) = 0

tan (0)

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

= - 0

Simplify

= 0

arctanh (0.8)

sin (2 \cdot 3.14)

arctanh (0.5)

arctan (3) - arcsec (- 2)

arccos (\frac{8}{26})