What is sin(arctan(-1/(mg))) ?

The solution to sin(arctan(-1/(mg))) is -(sqrt(m^2g^2+1))/(m^2g^2+1)

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simplify sin(arctan(-1/(mg)))

simplify

sin (arctan (- \frac{1}{m g}))

- \frac{m ^{2} g ^{2} + 1}{m ^{2} g ^{2} + 1}

Solution steps

sin (arctan (- \frac{1}{m g}))

Use the following identity:

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

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

Simplify

= - \frac{m ^{2} g ^{2} + 1}{m ^{2} g ^{2} + 1}

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What is sin(arctan(-1/(mg))) ?
The solution to sin(arctan(-1/(mg))) is -(sqrt(m^2g^2+1))/(m^2g^2+1)