What is the value of arctan(tan((4pi)/5)) ?

The value of arctan(tan((4pi)/5)) is -pi/5

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arctan(tan((4pi)/5))

arctan (tan (\frac{4 π}{5}))

- \frac{π}{5}

Decimal Notation

- 36

Solution steps

arctan (tan (\frac{4 π}{5}))

Use the inverse trig property:

- \frac{π}{5}

arctan (tan (\frac{4 π}{5}))

For

- \frac{π}{2} < x < \frac{π}{2}, a rc t an (t an (x)) = x

Rewrite using trig identities:

tan (\frac{4 π}{5}) = tan (- \frac{π}{5})

tan (\frac{4 π}{5})

tan (x + π \cdot k) = tan (x)

= tan (\frac{4 π}{5} - 1 π)

= tan (- \frac{π}{5})

= arctan (tan (- \frac{π}{5}))

- \frac{π}{2} < - \frac{π}{5} < \frac{π}{2}

= - \frac{π}{5}

= - \frac{π}{5}

arccos (cos (\frac{15 π}{4}))

sin (arctan (\frac{4}{3}))

cos (0.6)

arctan (\frac{8}{15})

sec (1 5^{\circ})

What is the value of arctan(tan((4pi)/5)) ?
The value of arctan(tan((4pi)/5)) is -pi/5