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

The value of arccot(tan((2pi)/3)) is (5pi)/6

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arccot(tan((2pi)/3))

arccot (tan (\frac{2 π}{3}))

\frac{5 π}{6}

Decimal Notation

150

Solution steps

arccot (tan (\frac{2 π}{3}))

Rewrite using trig identities:

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

tan (\frac{2 π}{3})

cot (\frac{π}{2} - x) = tan (x)

= cot (\frac{π}{2} - \frac{2 π}{3})

= cot (- \frac{π}{6})

= arccot (cot (- \frac{π}{6}))

Use the inverse trig property:

\frac{5 π}{6}

arccot (cot (- \frac{π}{6}))

For

0 < x < π, a rcco t (co t (x)) = x

Rewrite using trig identities:

cot (- \frac{π}{6}) = cot (\frac{5 π}{6})

cot (- \frac{π}{6})

cot (x + π \cdot k) = cot (x)

= cot (- \frac{π}{6} + 1 π)

= cot (\frac{5 π}{6})

= arccot (cot (\frac{5 π}{6}))

0 < \frac{5 π}{6} < π

= \frac{5 π}{6}

= \frac{5 π}{6}

sin (\frac{1}{0.1})

cos (arcsin (- \frac{5}{13}))

15 0^{22} + 3 5^{2} - 2 (150) (35) cos (11 0^{\circ})

sin (2 arccos (- \frac{12}{13}))

arctan (cot (\frac{π}{8}))

What is the value of arccot(tan((2pi)/3)) ?
The value of arccot(tan((2pi)/3)) is (5pi)/6