Flashcards
Rotations and Reflection
Cards in this deck (9)
- 1An AC rotation about the origin is given by....[cos(θ) -sin(θ][sin(θ) cos(θ)]
- 2If the rotation is CW, what will be different about θ?It will be -θ
- 3How do you recognize a rotation matrix?In the matrix [a b][c d] a->d will have the same signs and b->c will have opposite signs (signs = positive/negative)
Also the determinant will = 1 - 4What matrix represents a 30 degree AC rotation about the origin?[cos30 -sin30][sin30 cos30]
- 5What matrix represents a 45 degree rotation CW about the origin?[cos-45 -sin-45][sin-45 cos-45]
- 6A reflection in y=xtan(θ) is given by what? (note θ = angle from postive x axis)[cos2θ sin2θ][sin2θ -cos2θ]
- 7How do you recognize a reflection matrix?In the matrix [a b][c d] a->d will have opposite signs and b->c will have the same signs (signs = positive/negative)
Also the determinant will = -1 - 8Describe the method to work out: Find a matrix to reflect in y=3x1. tanθ=3, so θ=tan-1(3)
Multiply by 2 (as we need cos2θ/sin2θ)
Put the answer into cos and sin and put into matrix - 9If the thetas of cos and sin don't match, what must we do to make them match?For cos : 360 - 1st answer
For sin : 180 - 1st answer