Rotation of Axes: Homework Statement & Equation Solution

[Ledsnyder]

Homework Statement

THe x and y axes have been rotated about the origin through a 45 degree angle
to produce the X and Y axes.. Thus, a given point P (x,y) has coordinates in the first coordinate system and (X,Y) in the new coordinate system

The orignal equation is y=10sech(x).
What is the new equation in the new coordinate system?

Homework Equations

The Attempt at a Solution

x=
X cos(theta) - Y sin(theta)  y=
X sin(theta)- 
Y cos (theta)

These are for individual points but not for whole equations.

 

[Student100]

Have you drawn the picture?

 

[HallsofIvy]

Homework Statement

THe x and y axes have been rotated about the origin through a 45 degree angle
to produce the X and Y axes.. Thus, a given point P (x,y) has coordinates in the first coordinate system and (X,Y) in the new coordinate system

The orignal equation is y=10sech(x).
What is the new equation in the new coordinate system?

Homework Equations

The Attempt at a Solution

x= X cos(theta) - Y sin(theta) y= X sin(theta)- Y cos (theta)

These are for individual points but not for whole equations.

And you are told that Y= sech(X) so those equations become
x= X cos(45)- sech(X)sin(45), y= X sin(45)- sech(X) cos (45).

Eliminate X from those two equations.