Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.


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.

share|cite|improve this question
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
up vote 0 down vote accepted

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.

share|cite|improve this answer
Ok thanks! So other than that, it's correct? I must have looked at the wrong answer when I typed it out lol – ModdedLife Apr 21 '13 at 23:05
Yes, it looks good. – Cameron Buie Apr 21 '13 at 23:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.