# Did I solve all of the steps of this Trig question properly?

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 $\dfrac{1}{2}$

(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.

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Is predicted the one you obtained from the formula? If so, it is fine. How did you obtain the actual? The last two "actual" are not right. –  André Nicolas Apr 21 '13 at 22:57
I just plugged in my predicted values into the calculator for actual. I'm sort of confused with the wording of the question. It seems like it's asking me to find the equation of z, in terms of x, and then plug in the given x's to reach a predicted value.. then plug it in the calculator for the actual? –  ModdedLife Apr 21 '13 at 23:00
Cameron Buie undoubtedly has the right analysis. You calculated correctly, but interchanged the answers in the OP. –  André Nicolas Apr 21 '13 at 23:02

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.