How do you find the exact value of $tan(sin^-1(0.1))$ ?

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Answer 1 · 2017-04-13T03:06:22

$1/(3sqrt(11))$

Let $theta=sin^(-1)(0.1) Rightarrow sin(theta)=0.1=1/10=("Opposite")/("Hypotenuse")$

Let $("Opposite")=1$ and $("Hypotenuse")=10$ .

By Pythagorean Theorem,

$("Adjacent")=sqrt(10^2-1^2)=sqrt(99)=3sqrt(11)$

Hence,

$tan(sin^(-1)(0.1))=tan theta=("Opposite")/("Adjacent")=1/(3sqrt(11))$

I hope that this was clear.

How do you find the exact value of tan(sin^-1(0.1))tan(sin^-1(0.1))?