What is the value of sin(arctan(-3/2)) ?

The value of sin(arctan(-3/2)) is -(3sqrt(13))/(13)

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sin(arctan(-3/2))

sin (arctan (- \frac{3}{2}))

- \frac{3 13}{13}

Decimal Notation

- 0.83205 \dots

Solution steps

sin (arctan (- \frac{3}{2}))

Rewrite using trig identities:

sin (arctan (- \frac{3}{2})) = \frac{( - \frac{3}{2} ) 1 + ( - \frac{3}{2} ) ^{2}}{1 + ( - \frac{3}{2} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{3}{2} ) 1 + ( - \frac{3}{2} ) ^{2}}{1 + ( - \frac{3}{2} ) ^{2}}

= \frac{( - \frac{3}{2} ) 1 + ( - \frac{3}{2} ) ^{2}}{1 + ( - \frac{3}{2} ) ^{2}}

Simplify

= - \frac{3 13}{13}

\frac{6}{tan ( 3 7 ^{\circ} )} + \frac{6}{tan ( 4 7 ^{\circ} )}

arcsin (\frac{2.08}{9.8})

5 arcsin (- 1)

8 (cos (6 0^{\circ}) + i \cdot sin (6 0^{\circ}))

7 cos (5.8 \cdot π)

What is the value of sin(arctan(-3/2)) ?
The value of sin(arctan(-3/2)) is -(3sqrt(13))/(13)