What is the value of arctan(cot(6)) ?

The value of arctan(cot(6)) is (3pi-12)/2

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arctan(cot(6))

arctan (cot (6))

\frac{3 π - 12}{2}

Decimal

- 73.77

Solution steps

arctan (cot (6))

Rewrite using trig identities:

cot (6) = tan (\frac{π - 12}{2})

cot (6)

tan (\frac{π}{2} - x) = cot (x)

= tan (\frac{π}{2} - 6)

= tan (\frac{π - 12}{2})

= arctan (tan (\frac{π - 12}{2}))

Use the inverse trig property:

\frac{3 π - 12}{2}

arctan (tan (\frac{π - 12}{2}))

For

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

Rewrite using trig identities:

tan (\frac{π - 12}{2}) = tan (\frac{3 π - 12}{2})

tan (\frac{π - 12}{2})

tan (x + π \cdot k) = tan (x)

= tan (\frac{π - 12}{2} + 1 π)

= tan (\frac{3 π - 12}{2})

= arctan (tan (\frac{3 π - 12}{2}))

- \frac{π}{2} < \frac{3 π - 12}{2} < \frac{π}{2}

= \frac{3 π - 12}{2}

= \frac{3 π - 12}{2}