How do you find the exact value of $csc [arctan (- \frac{5}{12})]$ $csc[arctan(-5/12)]$ ?

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How do you find the exact value of $csc [arctan (- \frac{5}{12})]$ $csc[arctan(-5/12)]$ ?

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Answer 1 · 2016-03-06T14:19:07

$- \frac{13}{5}$ $-13/5$

Explanation:

Use definitions with respect to a right angled $△$ $triangle$ ABC.
The hypotenuse of the right angled $△$ $triangle$ ABC, with sides a and c including right angle B as 5 and 12, is 13.
$arctan (- \frac{5}{12}) = - arctan (\frac{5}{12}) = - a r c csc (\frac{13}{5})$ $arctan (-5/12) = -arctan (5/12) = - arc csc (13/5)$ .
csc arccsc (k) = k and csc( $- θ) = - csc (θ)$ $-theta)=-csc(theta)$
So, the answer is $- \frac{13}{5}$ $-13/5$ .

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How do you find the exact value of $csc [arctan (- \frac{5}{12})]$ $csc[arctan(-5/12)]$ ?

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