How do you evaluate $a r c cot (cot (- \frac{π}{4}))$ $arc cot(cot(-pi/4))$ without a calculator?

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How do you evaluate $a r c cot (cot (- \frac{π}{4}))$ $arc cot(cot(-pi/4))$ without a calculator?

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Answer 1 · 2016-10-13T17:29:57

see below

Explanation:

If we rewrite the original problem as $arctan (\frac{1}{tan (- \frac{π}{4})})$ $arctan(1/tan (-pi/4))$
Then
$arctan (\frac{1}{tan (- \frac{π}{4})}) = arctan (\frac{1}{- 1}) = arctan (- 1) = - \frac{π}{4}$ $arctan(1/tan (-pi/4))= arctan(1/-1)=arctan (-1)=-pi/4$

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How do you evaluate $a r c cot (cot (- \frac{π}{4}))$ $arc cot(cot(-pi/4))$ without a calculator?

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How do you evaluate arccot(cot(−π4))arc cot(cot(-pi/4)) without a calculator?

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How do you evaluate $a r c cot (cot (- \frac{π}{4}))$ $arc cot(cot(-pi/4))$ without a calculator?