What is the value of sin(arctan(5/33)) ?

The value of sin(arctan(5/33)) is (5sqrt(1114))/(1114)

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sin(arctan(5/33))

sin (arctan (\frac{5}{33}))

\frac{5 1114}{1114}

Decimal Notation

0.14980 \dots

Solution steps

sin (arctan (\frac{5}{33}))

Rewrite using trig identities:

sin (arctan (\frac{5}{33})) = \frac{( \frac{5}{33} ) 1 + ( \frac{5}{33} ) ^{2}}{1 + ( \frac{5}{33} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{5}{33} ) 1 + ( \frac{5}{33} ) ^{2}}{1 + ( \frac{5}{33} ) ^{2}}

= \frac{\frac{5}{33} 1 + ( \frac{5}{33} ) ^{2}}{1 + ( \frac{5}{33} ) ^{2}}

Simplify

= \frac{5 1114}{1114}

cos (\frac{2 π}{7}) + cos (\frac{4 π}{7}) + cos (\frac{6 π}{7})

arcsin (\frac{2.5}{10})

arctan (\frac{5}{2})

sinh (1) - sinh (0)

arctan (tan (\frac{123}{1000}))

What is the value of sin(arctan(5/33)) ?
The value of sin(arctan(5/33)) is (5sqrt(1114))/(1114)