Expert: Paul Klarreich - 3/6/2009

Question
QUESTION: Hello Paul. How do l find all points on this curve for which x=0: In(x^2+y^2)=2arcsin(x/y)

ANSWER: Questioner:   Nyasha
Category:  Calculus
Private:  No
 
Subject:  Points on a curve
Question:  Hello Paul. How do l find all points on this curve for which x=0: In(x^2+y^2)=2arcsin(x/y)


ln(y^2) = 2 arcsin(1/y)

2 ln(|y|) = 2 arcsin(1/y)

ln(|y|) = arcsin(1/y)

sin (ln |y|) = 1/y

sin (ln |y|) - 1/y = 0

Now you probably need some numerical work.


---------- FOLLOW-UP ----------

QUESTION: What happened to the x^2 ? It seems as if you just used the y^2 ?

Answer
Sorry -- correction posted.

Questioner:   Nyasha
Category:  Calculus
Private:  No
 
Subject:  Points on a curve
Question:  Hello Paul. How do l find all points on this curve for which x=0: In(x^2+y^2)=2arcsin(x/y)


ln( 0^2 + y^2) = 2 arcsin(0/y)

ln(y^2) = 2 arcsin(0)

2 ln(|y|) = 0

ln|y| = 0

|y| = 1

y = +- 1