Expert: Steve Holleran - 2/29/2008

Question
Hello and thank you in advance, Steve.  If I could see the steps laid out that would help the most.   
Solve for x algebraically:  tan^-1(x) = sin^-1(24/25)

Answer
Hi Douglas,

I think the easiest way to do this is to call sin^-1 (24/25) = A.

Then, you have :   sin A = 24/25

If you draw a first quadrant reference triangle, using angle A as the reference angle, label the opposite side 24 and the hypotenuse 25
(sin = opp/ hyp).  I'll try to diagram it here, without the hypotenuse
(if you draw this, just make OC the hypotenuse):
                            y
                            |
                            |    25    |C
                            |          |24
                            |          |
                   --------------------------   x
                            O          B

Then use the pythagorean theorem to find OB = 7.

Now, go back to your original equation.  Using the substitution I initially suggested, you can write:

                  tan^-1 x = A

so                    x = tan A   and using tan = opp/adj, you now have

                     x = 24/7.


I wish we could make diagrams easier on this site; I hope you can follow what I've outlined.  Any problems, let me know.

Steve