What is the value of sin(arctan(24/7)) ?

The value of sin(arctan(24/7)) is 24/25

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sin(arctan(24/7))

sin (arctan (\frac{24}{7}))

\frac{24}{25}

Decimal Notation

0.96

Solution steps

sin (arctan (\frac{24}{7}))

Rewrite using trig identities:

sin (arctan (\frac{24}{7})) = \frac{( \frac{24}{7} ) 1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{24}{7} ) 1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

= \frac{\frac{24}{7} 1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

Simplify

= \frac{24}{25}

cos (9 0^{\circ} + 4 5^{\circ})

csc (- 2)

arcsin (\frac{2 2}{3})

- sin (0.4)

- sin (0.5)

What is the value of sin(arctan(24/7)) ?
The value of sin(arctan(24/7)) is 24/25