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

The value of arctan(cot((2pi)/3)) is -pi/6

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arctan(cot((2pi)/3))

arctan (cot (\frac{2 π}{3}))

- \frac{π}{6}

Decimal Notation

- 30

Solution steps

arctan (cot (\frac{2 π}{3}))

Rewrite using trig identities:

cot (\frac{2 π}{3}) = tan (- \frac{π}{6})

cot (\frac{2 π}{3})

tan (\frac{π}{2} - x) = cot (x)

= tan (\frac{π}{2} - \frac{2 π}{3})

= tan (- \frac{π}{6})

= arctan (tan (- \frac{π}{6}))

Use the inverse trig property:

- \frac{π}{6}

arctan (tan (- \frac{π}{6}))

For

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

- \frac{π}{2} < - \frac{π}{6} < \frac{π}{2}

= - \frac{π}{6}

= - \frac{π}{6}

arccos (0.93)

(\frac{6}{e ^{4}})^{2} + (sin (4))^{4}

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tan (arcsin (\frac{7}{25}))

arccos (0.38)

What is the value of arctan(cot((2pi)/3)) ?
The value of arctan(cot((2pi)/3)) is -pi/6