What is the value of csc(arctan(2/3)) ?

The value of csc(arctan(2/3)) is (sqrt(13))/2

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csc(arctan(2/3))

csc (arctan (\frac{2}{3}))

\frac{13}{2}

Decimal Notation

1.80277 \dots

Solution steps

csc (arctan (\frac{2}{3}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{13}{2}

\frac{1.7}{sin ( 3 9 ^{\circ} )}

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

6 sin (- \frac{2 π}{3})

450 sin (4 5^{\circ})

arccos (- \frac{1}{5})

What is the value of csc(arctan(2/3)) ?
The value of csc(arctan(2/3)) is (sqrt(13))/2