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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tan(arcsin(-2/5))

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

- \frac{2 21}{21}

Decimal

- 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}

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