What is the value of csc(arctan(-3)) ?

The value of csc(arctan(-3)) is -(sqrt(10))/3

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csc(arctan(-3))

csc (arctan (- 3))

- \frac{10}{3}

Decimal Notation

- 1.05409 \dots

Solution steps

csc (arctan (- 3))

Rewrite using trig identities:

csc (arctan (- 3)) = \frac{1 + ( - 3 ) ^{2}}{( - 3 )}

Use the following identity:

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

= \frac{1 + ( - 3 ) ^{2}}{( - 3 )}

= \frac{1 + ( - 3 ) ^{2}}{- 3}

Simplify

= - \frac{10}{3}

sin (\frac{π}{5}) cos (\frac{π}{2}) + sin (\frac{π}{2}) cos (\frac{π}{5})

arccos (\frac{\frac{115}{7}}{\frac{5 754}{7}})

sec (arctan (\frac{7}{10}))

arctan (5.2)

arccos (\frac{- 30}{74 21})

What is the value of csc(arctan(-3)) ?
The value of csc(arctan(-3)) is -(sqrt(10))/3