What is the value of csc(arctan(-5/12)) ?

The value of csc(arctan(-5/12)) is -13/5

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csc(arctan(-5/12))

csc (arctan (- \frac{5}{12}))

- \frac{13}{5}

Decimal Notation

- 2.6

Solution steps

csc (arctan (- \frac{5}{12}))

Rewrite using trig identities:

csc (arctan (- \frac{5}{12})) = \frac{1 + ( - \frac{5}{12} ) ^{2}}{( - \frac{5}{12} )}

Use the following identity:

csc (arctan (x)) = \frac{1 + x ^{2}}{x}

= \frac{1 + ( - \frac{5}{12} ) ^{2}}{( - \frac{5}{12} )}

= \frac{1 + ( - \frac{5}{12} ) ^{2}}{- \frac{5}{12}}

Simplify

= - \frac{13}{5}

- 3 sin (\frac{3 π}{2})

3 cos (4 0^{\circ})

csc (\frac{13 π}{4})

sin (3 \cdot 0)

cos (15 π)

What is the value of csc(arctan(-5/12)) ?
The value of csc(arctan(-5/12)) is -13/5