What is the value of sin(arctan(-7/9)) ?

The value of sin(arctan(-7/9)) is -(7sqrt(130))/(130)

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sin(arctan(-7/9))

sin (arctan (- \frac{7}{9}))

- \frac{7 130}{130}

Decimal Notation

- 0.61394 \dots

Solution steps

sin (arctan (- \frac{7}{9}))

Rewrite using trig identities:

sin (arctan (- \frac{7}{9})) = \frac{( - \frac{7}{9} ) 1 + ( - \frac{7}{9} ) ^{2}}{1 + ( - \frac{7}{9} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{7}{9} ) 1 + ( - \frac{7}{9} ) ^{2}}{1 + ( - \frac{7}{9} ) ^{2}}

= \frac{( - \frac{7}{9} ) 1 + ( - \frac{7}{9} ) ^{2}}{1 + ( - \frac{7}{9} ) ^{2}}

Simplify

= - \frac{7 130}{130}

- sin (2 (0)) \cdot 2

sin^{2} (3) + cos^{2} (3)

sin (arcsin (\frac{3}{5}) - arctan (\frac{12}{5}))

arctan (- \frac{3}{3 3})

cos (0 + π)

What is the value of sin(arctan(-7/9)) ?
The value of sin(arctan(-7/9)) is -(7sqrt(130))/(130)