What is the value of arccot(tan(6)) ?

The value of arccot(tan(6)) is (5pi-12)/2

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arccot(tan(6))

arccot (tan (6))

\frac{5 π - 12}{2}

Decimal Notation

106.23

Solution steps

arccot (tan (6))

Rewrite using trig identities:

tan (6) = cot (\frac{π - 12}{2})

tan (6)

cot (\frac{π}{2} - x) = tan (x)

= cot (\frac{π}{2} - 6)

= cot (\frac{π - 12}{2})

= arccot (cot (\frac{π - 12}{2}))

Use the inverse trig property:

\frac{5 π - 12}{2}

arccot (cot (\frac{π - 12}{2}))

For

0 < x < π, a rcco t (co t (x)) = x

Rewrite using trig identities:

cot (\frac{π - 12}{2}) = cot (\frac{5 π - 12}{2})

cot (\frac{π - 12}{2})

cot (x + π \cdot k) = cot (x)

= cot (\frac{π - 12}{2} + 2 π)

= cot (\frac{5 π - 12}{2})

= arccot (cot (\frac{5 π - 12}{2}))

0 < \frac{5 π - 12}{2} < π

= \frac{5 π - 12}{2}

= \frac{5 π - 12}{2}

- 2 cos (\frac{11 π}{6})

arcsin (\frac{50 sin ( 2 5 ^{\circ} )}{35})

\frac{cos ( 7 π )}{6}

5 cos (5 6^{\circ})

8 cos (5 3^{\circ})