What is the value of sin(arctan(-5/3)) ?

The value of sin(arctan(-5/3)) is -(5sqrt(34))/(34)

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sin(arctan(-5/3))

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

- \frac{5 34}{34}

Decimal Notation

- 0.85749 \dots

Solution steps

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

Rewrite using trig identities:

sin (arctan (- \frac{5}{3})) = \frac{( - \frac{5}{3} ) 1 + ( - \frac{5}{3} ) ^{2}}{1 + ( - \frac{5}{3} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{5}{3} ) 1 + ( - \frac{5}{3} ) ^{2}}{1 + ( - \frac{5}{3} ) ^{2}}

= \frac{( - \frac{5}{3} ) 1 + ( - \frac{5}{3} ) ^{2}}{1 + ( - \frac{5}{3} ) ^{2}}

Simplify

= - \frac{5 34}{34}

tan (arcsin (\frac{3}{5}) + arccos (- 1))

arccos (\frac{24}{25})

sin^{8} (\frac{π}{2})

sin (3 0^{\circ}) + sin (3 0^{\circ})

6 sin (8 0^{\circ})

What is the value of sin(arctan(-5/3)) ?
The value of sin(arctan(-5/3)) is -(5sqrt(34))/(34)