What is the value of csc(arctan(-8/9)) ?

The value of csc(arctan(-8/9)) is -(sqrt(145))/8

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csc(arctan(-8/9))

csc (arctan (- \frac{8}{9}))

- \frac{145}{8}

Decimal Notation

- 1.50519 \dots

Solution steps

csc (arctan (- \frac{8}{9}))

Rewrite using trig identities:

csc (arctan (- \frac{8}{9})) = \frac{1 + ( - \frac{8}{9} ) ^{2}}{( - \frac{8}{9} )}

Use the following identity:

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

= \frac{1 + ( - \frac{8}{9} ) ^{2}}{( - \frac{8}{9} )}

= \frac{1 + ( - \frac{8}{9} ) ^{2}}{- \frac{8}{9}}

Simplify

= - \frac{145}{8}

sin^{2} (21 0^{\circ})

sin (4 5^{\circ}) cos (4 5^{\circ})

sin (23 0^{\circ})

csc (5 0^{\circ})

cos (\frac{7}{6} π)

What is the value of csc(arctan(-8/9)) ?
The value of csc(arctan(-8/9)) is -(sqrt(145))/8