Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$$ \arctan\left(\frac{x}{\sqrt{a^2-x^2}}\right)$$

Hi, I am not able to solve this problem from last 1 hour. Please help me to solve this question. As I can solve simple inverse trigonometric functions.

share|improve this question
1  
Set $x = a \sin(\phi)$, and simplify the argument of the $\arctan$. Are you assuming $0<x<a$? –  Sasha Aug 23 '12 at 15:38
add comment

1 Answer 1

Think geometrically. What is the $\tan(\phi)$ ?

enter image description here

share|improve this answer
1  
Please, can you tell me the name of the software which you use to draw these pictures. I try to use GeoGebra and a friend recommend me to use MetaPost but I have some issues to use these software correctly. Thanks :) –  Iuli Aug 23 '12 at 15:57
    
@Iuli I used Mathematica. The command can be found here. –  Sasha Aug 23 '12 at 16:07
    
So $\arctan\dfrac{x}{\sqrt{a^2-x^2}}=\arccos\dfrac x a$. –  Michael Hardy Aug 23 '12 at 20:46
1  
@MichaelHardy I think it should be $\arcsin \frac{x}{a}$, instead. –  Sasha Aug 23 '12 at 21:01
    
@Sasha : You're right: I'm accustomed to pictures in which the "opposite" side is vertical and the "adjacent" side horizontal. –  Michael Hardy Aug 23 '12 at 21:05
add comment

Your Answer

 
discard

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.