What is the value of sin(arctan(-8)) ?

The value of sin(arctan(-8)) is -(8sqrt(65))/(65)

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sin(arctan(-8))

sin (arctan (- 8))

- \frac{8 65}{65}

Decimal Notation

- 0.99227 \dots

Solution steps

sin (arctan (- 8))

Rewrite using trig identities:

sin (arctan (- 8)) = \frac{( - 8 ) 1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

Use the following identity:

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

= \frac{( - 8 ) 1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

= \frac{( - 8 ) 1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

Simplify

= - \frac{8 65}{65}

cot (\frac{11 π}{4})

cos (\frac{3 π}{10})

csc (- \frac{5 π}{3})

sin (\frac{15 π}{2})

cos (\frac{1}{4} π)

What is the value of sin(arctan(-8)) ?
The value of sin(arctan(-8)) is -(8sqrt(65))/(65)