What is the value of tan(arcsin(-5/6)) ?

The value of tan(arcsin(-5/6)) is -(5sqrt(11))/(11)

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tan(arcsin(-5/6))

tan (arcsin (- \frac{5}{6}))

- \frac{5 11}{11}

Decimal Notation

- 1.50755 \dots

Solution steps

tan (arcsin (- \frac{5}{6}))

Rewrite using trig identities:

tan (arcsin (- \frac{5}{6})) = \frac{( - \frac{5}{6} ) 1 - ( - \frac{5}{6} ) ^{2}}{1 - ( - \frac{5}{6} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{5}{6} ) 1 - ( - \frac{5}{6} ) ^{2}}{1 - ( - \frac{5}{6} ) ^{2}}

= \frac{( - \frac{5}{6} ) 1 - ( - \frac{5}{6} ) ^{2}}{1 - ( - \frac{5}{6} ) ^{2}}

Simplify

= - \frac{5 11}{11}

cos (\frac{π}{2}) - cos (0)

\frac{14 \cdot 15 \cdot sin ( 12 5 ^{\circ} )}{2}

1 tan (3 0^{\circ})

cos (85 5^{\circ})

2 \cdot sin (2 0^{\circ})

What is the value of tan(arcsin(-5/6)) ?
The value of tan(arcsin(-5/6)) is -(5sqrt(11))/(11)