What is the value of tan(arcsin(-2/3)) ?

The value of tan(arcsin(-2/3)) is -(2sqrt(5))/5

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tan(arcsin(-2/3))

tan (arcsin (- \frac{2}{3}))

- \frac{2 5}{5}

Decimal Notation

- 0.89442 \dots

Solution steps

tan (arcsin (- \frac{2}{3}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{2 5}{5}

sin (9 1^{\circ})

tan (\frac{2 π}{7})

csc (60 0^{\circ})

- sin (6)

arctan (\frac{15}{13})

What is the value of tan(arcsin(-2/3)) ?
The value of tan(arcsin(-2/3)) is -(2sqrt(5))/5