Solving Rotation Matrices Urgently: cos(pi/4) -sin(pi/4) sin(pi/4) cos(pi/4)

In summary, a rotation matrix is a square matrix used to describe the rotation of an object in a three-dimensional space. It is typically represented using cosine and sine values and is used to determine the orientation and position of an object after a rotation transformation. The values cos(pi/4) and sin(pi/4) in the given example represent a rotation of 45 degrees around the z-axis. The urgency of solving rotation matrices varies depending on the specific application or problem, but it is an important skill for scientists and mathematicians to have.
  • #1
rrm74001
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[URGENT] Rotation Matrices

Homework Statement



http://e.imagehost.org/0661/Screen_shot_2010-03-09_at_12_37_44_AM.png

Homework Equations



Rotation Matrix:
cos(theta) -sin(theta)
sin(theta) cos(theta)

The Attempt at a Solution



I understand 2a:

cos(pi/4) -sin(pi/4)
sin(pi/4) cos(pi/4)

But I am not sure what 2b is looking for. Please help?

Thank you in advance for your help!
 
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  • #2


The matrix you wrote is a rotation matrix, which rotates a vector but leaves its length unchanged. You need a matrix which doubles the length as well. Try to find such one. ehild
 
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1. What is a rotation matrix?

A rotation matrix is a mathematical tool used to describe the rotation of an object in a three-dimensional space. It is a square matrix that represents a rotation transformation.

2. How is a rotation matrix represented?

A rotation matrix is typically represented using a combination of cosine and sine values, as shown in the example: cos(theta) -sin(theta) sin(theta) cos(theta). This represents a rotation around the z-axis by an angle of theta.

3. What is the purpose of solving rotation matrices?

The main purpose of solving rotation matrices is to determine the orientation and position of an object after a rotation transformation. This is useful in various fields such as computer graphics, robotics, and physics.

4. What is the significance of the values cos(pi/4) and sin(pi/4) in the given example?

The values cos(pi/4) and sin(pi/4) represent the cosine and sine of the angle pi/4 (45 degrees) respectively. These values are commonly used in rotation matrices as they correspond to a rotation of 45 degrees around the z-axis.

5. How urgent is it to solve rotation matrices?

The urgency of solving rotation matrices depends on the specific application or problem at hand. In some cases, it may be necessary to solve rotation matrices quickly, while in others it may not be as urgent. However, it is an important skill for any scientist or mathematician to have in their toolkit.

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