What is the value of csc(arctan(-2)) ?

The value of csc(arctan(-2)) is -(sqrt(5))/2

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csc(arctan(-2))

csc (arctan (- 2))

- \frac{5}{2}

Decimal Notation

- 1.11803 \dots

Solution steps

csc (arctan (- 2))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{5}{2}

2 sin (\frac{4 π}{3})

csc (10 5^{\circ})

cos (2) (\frac{π}{2})

arcsin (- \frac{1}{4})

cos (3 \frac{π}{2})

What is the value of csc(arctan(-2)) ?
The value of csc(arctan(-2)) is -(sqrt(5))/2