What is the value of tan(arcsin((-12)/(13))) ?

The value of tan(arcsin((-12)/(13))) is -12/5

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tan(arcsin((-12)/(13)))

tan (arcsin (\frac{- 12}{13}))

- \frac{12}{5}

Decimal

- 2.4

Solution steps

tan (arcsin (\frac{- 12}{13}))

Rewrite using trig identities:

tan (arcsin (\frac{- 12}{13})) = \frac{( \frac{- 12}{13} ) 1 - ( \frac{- 12}{13} ) ^{2}}{1 - ( \frac{- 12}{13} ) ^{2}}

Use the following identity:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

= \frac{( \frac{- 12}{13} ) 1 - ( \frac{- 12}{13} ) ^{2}}{1 - ( \frac{- 12}{13} ) ^{2}}

= \frac{\frac{- 12}{13} 1 - ( \frac{- 12}{13} ) ^{2}}{1 - ( \frac{- 12}{13} ) ^{2}}

Simplify

= - \frac{12}{5}

What is the value of tan(arcsin((-12)/(13))) ?
The value of tan(arcsin((-12)/(13))) is -12/5