Thanks to some help from the community, I think I did this problem correctly, but I would like someone to confirm that I indeed do it right. Thanks.
Question:
Let $0 \le x \le 1$.
(i.) Find the value of $z = \tan{(\arcsin{x})}$ in terms of $x$.
(ii.) Use the given values of $x$ to validate your result from part (i) by comparing your predicted value of $z$ to the result obtained by your calculator.
- Given values of $x$: $(\dfrac{\sqrt2}{2})$, $\dfrac{\sqrt3}{2}$, and $\dfrac{1}{2}$
My Answer:
(i.) $z = \tan{(\arcsin{x})} = \dfrac{x}{\sqrt{1-x^2}}$
$x=\dfrac{\sqrt{2}}{2}$: Predicted z: $\dfrac{\sqrt{2}}{2\sqrt{1/2}}$ Actual z: $1$
$x=\dfrac{\sqrt{3}}{2}$: Predicted z: $\sqrt{3}$ Actual z: $.57735$
$x=\dfrac{1}{2}$: Predicted z: $\dfrac{1}{\sqrt{3}}$ Actual z: $1.7321$
Sorry, I wasn't sure how to do the coding to make this actually look like equations.
But could somebody point out any mistakes that I may have made? Thanks.
Note that $2\sqrt{\frac12}=\sqrt{2}$, so your prediction and actual match in that case. I'm not sure how, but you've gotten the "actual" answers for the other two switched.