Rotation of Axis to Eliminate Cross-Product Term

In summary, the conversation is about how to eliminate the cross-product term in a given work by making a rotation of axis. The person asking the question has provided a picture as an example and is seeking help in understanding where the numbers in the solution come from. They mention a 30/60/90 triangle and ask for clarification. A response has been provided in a picture form.
  • #1
rcmango
234
0

Homework Statement



The question si the make a rotation of axis to elmininate the cross-product term in the work i provided in this pic: http://img295.imageshack.us/img295/9579/untitledtu4.png

Homework Equations





The Attempt at a Solution



I've drawn of the example in the pic I've given a link.

my questions:

how do i know that 2 theta = pi/3 and theta is pi/6

where does the sqrt(3)/2 and 1/2 come from?

i know there is some kind of 30/60/90 triangle going on here i think.
can someone please help me understand where the numbers are coming from.

if you expand the pic its MUCH easier to view.

thankyou.
 
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  • #2
a response in your method =p

http://img96.imageshack.us/img96/1745/sresponsewm5.jpg
 
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FAQ: Rotation of Axis to Eliminate Cross-Product Term

What is the rotation of axis question?

The rotation of axis question is a mathematical concept that involves rotating a coordinate system or a set of axes in a specific direction and angle to better understand the relationship between different variables.

Why is the rotation of axis question important?

The rotation of axis question is important because it allows us to simplify and solve complex mathematical problems, such as finding the equation of a circle or calculating the area under a curve. It also helps us visualize and interpret data in different ways.

What are the different types of rotations of axis?

There are three types of rotations of axis:
1. Rotation about the origin: where the axes are rotated around the origin point
2. Rotation about a fixed point: where the axes are rotated around a specific point in the coordinate plane
3. Rotation about an arbitrary point: where the axes are rotated around a point that is not on the coordinate plane.

How do you perform a rotation of axis?

To perform a rotation of axis, you need to determine the direction and angle of rotation. Then, you can use a rotation matrix or a set of transformation equations to rotate the axes. You can also use a graphing calculator or software to perform the rotation for you.

What are some real-world applications of the rotation of axis question?

The rotation of axis question has many real-world applications, such as:
- GPS navigation systems use rotation of axis to accurately determine a user's location
- In physics, rotation of axis is used to calculate the moment of inertia of objects
- In engineering, rotation of axis is used to analyze and design structures and machines
- In computer graphics, rotation of axis is used to create 3D animations and models.

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