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

The value of csc(arctan(2/5)) is (sqrt(29))/2

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csc(arctan(2/5))

csc (arctan (\frac{2}{5}))

\frac{29}{2}

Decimal Notation

2.69258 \dots

Solution steps

csc (arctan (\frac{2}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{29}{2}

cos (π) + π

cos (arcsin (\frac{1}{2}) + arccos (\frac{4}{5}))

(cos (\frac{π}{4}) + i sin (\frac{π}{4}))^{3}

309.4 \cdot (\frac{sin ( 42.3 1 ^{\circ} )}{238.99})

arccos (\frac{8}{13})

What is the value of csc(arctan(2/5)) ?
The value of csc(arctan(2/5)) is (sqrt(29))/2