Evaluate tan(sin^-1 (-4/5))

Here, we are required to evaluate tan(sin^-1 (-4/5)).

tan(sin^-1 (-4/5)) = (-4/3)

Sin^-1 (-4/5) = θ

Therefore; ultimately Sin θ = (-4/5)

Since; Sine = opposite / hypothenus

Therefore, adj = √(5²) - (4²)

adj = 3.

However, since tan(sin^-1 (-4/5)) = tan θ

Therefore, tan θ = 4/3

However, since sin θ and tan θ are only negative in the fourth quarter;

Therefore, tan θ = (-4/3)

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