What is the value of tan(arcsin((-3)/4)) ?

The value of tan(arcsin((-3)/4)) is -(3sqrt(7))/7

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tan(arcsin((-3)/4))

tan (arcsin (\frac{- 3}{4}))

- \frac{3 7}{7}

Decimal Notation

- 1.13389 \dots

Solution steps

tan (arcsin (\frac{- 3}{4}))

Rewrite using trig identities:

tan (arcsin (\frac{- 3}{4})) = \frac{( \frac{- 3}{4} ) 1 - ( \frac{- 3}{4} ) ^{2}}{1 - ( \frac{- 3}{4} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{- 3}{4} ) 1 - ( \frac{- 3}{4} ) ^{2}}{1 - ( \frac{- 3}{4} ) ^{2}}

= \frac{\frac{- 3}{4} 1 - ( \frac{- 3}{4} ) ^{2}}{1 - ( \frac{- 3}{4} ) ^{2}}

Simplify

= - \frac{3 7}{7}

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

arctan (32)

12 \cdot cos (4 0^{\circ})

sin (π) + π

arctan (\frac{20}{16})

What is the value of tan(arcsin((-3)/4)) ?
The value of tan(arcsin((-3)/4)) is -(3sqrt(7))/7