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

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

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tan(arcsin((-5)/(13)))

tan (arcsin (\frac{- 5}{13}))

- \frac{5}{12}

Decimal Notation

- 0.41666 \dots

Solution steps

tan (arcsin (\frac{- 5}{13}))

Rewrite using trig identities:

tan (arcsin (\frac{- 5}{13})) = \frac{( \frac{- 5}{13} ) 1 - ( \frac{- 5}{13} ) ^{2}}{1 - ( \frac{- 5}{13} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{- 5}{13} ) 1 - ( \frac{- 5}{13} ) ^{2}}{1 - ( \frac{- 5}{13} ) ^{2}}

= \frac{\frac{- 5}{13} 1 - ( \frac{- 5}{13} ) ^{2}}{1 - ( \frac{- 5}{13} ) ^{2}}

Simplify

= - \frac{5}{12}

arctan (\frac{- 31}{22})

e^{2} cos (0)

arcsin (\frac{- 1}{3})

sin (12 0^{\circ}) + tan (12 0^{\circ})

\frac{1}{1 - cos ( 1 )}

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