What is the value of tan(arcsin(-4/5)) ?

The value of tan(arcsin(-4/5)) is -4/3

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tan(arcsin(-4/5))

tan (arcsin (- \frac{4}{5}))

- \frac{4}{3}

Decimal Notation

- 1.33333 \dots

Solution steps

tan (arcsin (- \frac{4}{5}))

Rewrite using trig identities:

tan (arcsin (- \frac{4}{5})) = \frac{( - \frac{4}{5} ) 1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{4}{5} ) 1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

= \frac{( - \frac{4}{5} ) 1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

Simplify

= - \frac{4}{3}

sin^{2} (\frac{π}{3})

tan (x) = 3

csc (\frac{5 π}{4})

cos (\frac{11 π}{12})

csc (\frac{5 π}{6})