What is the value of sin(arctan(4/5)) ?

The value of sin(arctan(4/5)) is (4sqrt(41))/(41)

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sin(arctan(4/5))

sin (arctan (\frac{4}{5}))

\frac{4 41}{41}

Decimal Notation

0.62469 \dots

Solution steps

sin (arctan (\frac{4}{5}))

Rewrite using trig identities:

sin (arctan (\frac{4}{5})) = \frac{( \frac{4}{5} ) 1 + ( \frac{4}{5} ) ^{2}}{1 + ( \frac{4}{5} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{4}{5} ) 1 + ( \frac{4}{5} ) ^{2}}{1 + ( \frac{4}{5} ) ^{2}}

= \frac{\frac{4}{5} 1 + ( \frac{4}{5} ) ^{2}}{1 + ( \frac{4}{5} ) ^{2}}

Simplify

= \frac{4 41}{41}

csc (- 54 0^{\circ})

tan (e)

2 - 2 cos (π)

arctan (tan (- \frac{19 π}{18}))

15 \cdot sin (2 5^{\circ})

What is the value of sin(arctan(4/5)) ?
The value of sin(arctan(4/5)) is (4sqrt(41))/(41)