How do you find the value of tan(sin^-1(1/3))?

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Answer 1 · 2018-03-29T18:01:26

From the reference Inverse Trigonometric Functions, we obtain the identity:

#tan(sin^-1(x)) = x/sqrt(1-x^2)#

Substitute #x = 1/3#

#tan(sin^-1(1/3)) = (1/3)/sqrt(1-(1/3)^2)#

#tan(sin^-1(1/3)) = 1/(3sqrt(1-(1/3)^2))#

#tan(sin^-1(1/3)) = 1/sqrt(9-1)#

#tan(sin^-1(1/3)) = 1/sqrt8#

#tan(sin^-1(1/3)) = 1/(2sqrt2)#

#tan(sin^-1(1/3)) = sqrt2/4#