What is the value of csc(arctan(-1)) ?

The value of csc(arctan(-1)) is -sqrt(2)

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csc(arctan(-1))

csc (arctan (- 1))

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

csc (arctan (- 1))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - 2

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