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.