What is the value of arccot(cot(-10)) ?

The value of arccot(cot(-10)) is (17pi)/(18)

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arccot(cot(-10))

arccot (cot (- 1 0^{\circ}))

\frac{17 π}{18}

Decimal Notation

170

Solution steps

arccot (cot (- 1 0^{\circ}))

Use the inverse trig property:

17 0^{\circ}

arccot (cot (- 1 0^{\circ}))

For

0 < x < 18 0^{\circ}, a rcco t (co t (x)) = x

Rewrite using trig identities:

cot (- 1 0^{\circ}) = cot (17 0^{\circ})

cot (- 1 0^{\circ})

cot (x + 18 0^{\circ} \cdot k) = cot (x)

= cot (- 1 0^{\circ} + 18 0^{\circ})

= cot (17 0^{\circ})

= arccot (cot (17 0^{\circ}))

0 < 17 0^{\circ} < 18 0^{\circ}

= 17 0^{\circ}

= 17 0^{\circ}

2 sin (- 7 0^{\circ})

cos (6 0^{\circ}) cos (6 5^{\circ}) - sin (6 0^{\circ}) sin (6 5^{\circ})

arcsin (\frac{0}{3})

cos (\frac{37 π}{6})

\frac{2}{sin ( 3 7 ^{\circ} )}

What is the value of arccot(cot(-10)) ?
The value of arccot(cot(-10)) is (17pi)/(18)