What is the value of arctan(tan((4pi)/3)) ?

The value of arctan(tan((4pi)/3)) is pi/3

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arctan(tan((4pi)/3))

arctan (tan (\frac{4 π}{3}))

\frac{π}{3}

Decimal Notation

60

Solution steps

arctan (tan (\frac{4 π}{3}))

Use the inverse trig property:

\frac{π}{3}

arctan (tan (\frac{4 π}{3}))

For

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

Rewrite using trig identities:

tan (\frac{4 π}{3}) = tan (\frac{π}{3})

tan (\frac{4 π}{3})

tan (x + π \cdot k) = tan (x)

= tan (\frac{4 π}{3} - 1 π)

= tan (\frac{π}{3})

= arctan (tan (\frac{π}{3}))

- \frac{π}{2} < \frac{π}{3} < \frac{π}{2}

= \frac{π}{3}

= \frac{π}{3}

sec (- \frac{7 π}{6})

tan (arcsin (\frac{5}{13}))

arccos (cos (\frac{3 π}{2}))

sec (\frac{10 π}{3})

arcsin (9)

What is the value of arctan(tan((4pi)/3)) ?
The value of arctan(tan((4pi)/3)) is pi/3