tan(sin-1 12/13)

Question

Find the exact value of the expression

Answer 1

Let x=sin^-1(12/13), so sin(x)=12/13 and we have to find tan(x).

sin(x)=12/13=opposite/hypotenuse in right triangle.

tan(x)=opposite/adjacent.

adjacent²+opposite²=hypotenuse² (Pythagoras),

adjacent²+12²=13²,

adjacent²+144=169,

adjacent²=169-144=25,

adjacent=5,

tan(x)=12/5=2.4, so tan(sin^-1(12/13))=2.4.