What is the value of sin(arctan(7/4)) ?

The value of sin(arctan(7/4)) is (7sqrt(65))/(65)

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sin(arctan(7/4))

sin (arctan (\frac{7}{4}))

\frac{7 65}{65}

Decimal Notation

0.86824 \dots

Solution steps

sin (arctan (\frac{7}{4}))

Rewrite using trig identities:

sin (arctan (\frac{7}{4})) = \frac{( \frac{7}{4} ) 1 + ( \frac{7}{4} ) ^{2}}{1 + ( \frac{7}{4} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{7}{4} ) 1 + ( \frac{7}{4} ) ^{2}}{1 + ( \frac{7}{4} ) ^{2}}

= \frac{\frac{7}{4} 1 + ( \frac{7}{4} ) ^{2}}{1 + ( \frac{7}{4} ) ^{2}}

Simplify

= \frac{7 65}{65}

- 5 sin (0)

csc (\frac{11 π}{2})

arccos (\frac{13}{6 86})

15 cos (6 0^{\circ})

arctan (- 9)

What is the value of sin(arctan(7/4)) ?
The value of sin(arctan(7/4)) is (7sqrt(65))/(65)