What is the value of arctan(tan((2pi)/3)) ?

The value of arctan(tan((2pi)/3)) is -pi/3

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arctan(tan((2pi)/3))

arctan (tan (\frac{2 π}{3}))

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

arctan (tan (\frac{2 π}{3}))

Use the inverse trig property:

- \frac{π}{3}

arctan (tan (\frac{2 π}{3}))

For

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

Rewrite using trig identities:

tan (\frac{2 π}{3}) = tan (- \frac{π}{3})

tan (\frac{2 π}{3})

tan (x + π \cdot k) = tan (x)

= tan (\frac{2 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}

cos (- \frac{2 π}{3})

sin (3 0^{\circ})

cos (\frac{5 π}{3})

cot (12 0^{\circ})

sin (2 x) + sin (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the value of arctan(tan((2pi)/3)) ?
The value of arctan(tan((2pi)/3)) is -pi/3