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

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

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tan(arcsin(-3/5))

tan (arcsin (- \frac{3}{5}))

- \frac{3}{4}

Decimal Notation

- 0.75

Solution steps

tan (arcsin (- \frac{3}{5}))

Rewrite using trig identities:

tan (arcsin (- \frac{3}{5})) = \frac{( - \frac{3}{5} ) 1 - ( - \frac{3}{5} ) ^{2}}{1 - ( - \frac{3}{5} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{3}{5} ) 1 - ( - \frac{3}{5} ) ^{2}}{1 - ( - \frac{3}{5} ) ^{2}}

= \frac{( - \frac{3}{5} ) 1 - ( - \frac{3}{5} ) ^{2}}{1 - ( - \frac{3}{5} ) ^{2}}

Simplify

= - \frac{3}{4}

sec^{2} (x) - 2 = 0

cos (2 t) = \frac{- 3}{2}

cos (2 x) = \frac{3}{2}, 0 \leq x \leq 2 π

arcsin (\frac{4}{5})

cos (x) = \frac{3}{4}