Simplifying the Parameter Elimination for X=sin(t) and y=csc(x)

  • Thread starter Thread starter Ura
  • Start date Start date
  • Tags Tags
    Parameter
Click For Summary
SUMMARY

The discussion focuses on the parameter elimination for the equations X=sin(t) and y=csc(x). The correct approach involves substituting t with arcsin(x), leading to the equation y=csc(arcsin(x)). A participant questions whether the second equation should be y=csc(t) instead, indicating a potential typo in the original problem statement. The consensus is that the parameter elimination can be simplified using the correct substitutions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosecant.
  • Familiarity with parameterization in calculus.
  • Knowledge of inverse trigonometric functions, particularly arcsin.
  • Basic algebraic manipulation skills for simplifying equations.
NEXT STEPS
  • Study the properties of inverse trigonometric functions, focusing on arcsin and its applications.
  • Learn about parameterization techniques in calculus and their implications in curve analysis.
  • Explore the relationship between trigonometric identities and their inverse functions.
  • Practice problems involving parameter elimination in various contexts, such as polar coordinates.
USEFUL FOR

Students studying calculus, particularly those focusing on parameterization and curve analysis, as well as educators looking for examples of parameter elimination techniques.

Ura
Messages
1
Reaction score
0

Homework Statement



Eliminate the parameter to find a Cartesian equation for the curve.
X=sin(t), y=csc(x)

Homework Equations





The Attempt at a Solution


Is this correct?
X=sin(t)
Arcsin(x)=t
So y=csc(arcsin(x)

Can I simplify it further?
 
Physics news on Phys.org
is the second equation a typo: x=sin(t), y=csc(x) should it be y=csc(t)?

from your substitution it appears that is what you think it is.
 

Similar threads

  • · Replies 27 ·
Replies
27
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 1 ·
Replies
1
Views
9K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
2K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K