What is the value of tan(arcsin(-2/5)) ?

The value of tan(arcsin(-2/5)) is -(2sqrt(21))/(21)

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tan(arcsin(-2/5))

tan (arcsin (- \frac{2}{5}))

- \frac{2 21}{21}

Decimal Notation

- 0.43643 \dots

Solution steps

tan (arcsin (- \frac{2}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{2 21}{21}

arctan (2) + arctan (\frac{1}{2})

arctan (- 5.5)

cos (4 5^{\circ}) (sin (3 0^{\circ}) + tan (6 0^{\circ}))

cos (16 5^{\circ}) - cos (1 5^{\circ})

2 sin (3 0^{\circ}) + 3 cos (6 0^{\circ}) - 3 tan (4 5^{\circ})

What is the value of tan(arcsin(-2/5)) ?
The value of tan(arcsin(-2/5)) is -(2sqrt(21))/(21)