What is the value of sin(arctan(-4/3)) ?

The value of sin(arctan(-4/3)) is -4/5

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sin(arctan(-4/3))

sin (arctan (- \frac{4}{3}))

- \frac{4}{5}

Decimal Notation

- 0.8

Solution steps

sin (arctan (- \frac{4}{3}))

Rewrite using trig identities:

sin (arctan (- \frac{4}{3})) = \frac{( - \frac{4}{3} ) 1 + ( - \frac{4}{3} ) ^{2}}{1 + ( - \frac{4}{3} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{4}{3} ) 1 + ( - \frac{4}{3} ) ^{2}}{1 + ( - \frac{4}{3} ) ^{2}}

= \frac{( - \frac{4}{3} ) 1 + ( - \frac{4}{3} ) ^{2}}{1 + ( - \frac{4}{3} ) ^{2}}

Simplify

= - \frac{4}{5}

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arcsin (sin (- \frac{5 π}{3}))

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