Question

Which angle of rotation is determined by the matrix below?{1/2 -sqrt3/2 sqrt3/2 1/2] 30° 60° 120° 300°

Answer 1

B----- 60

Explanation:

Answer 2

60°

Explanation:

You have the rotation matrix ...

`\left[\begin{array}{cc}cos(\theta)&-sin(\theta)\\sin(\theta)&cos(\theta)\end{array}\right]=\left[\begin{array}{cc}(1)/(2)&-(√(3))/(2)\\(√(3))/(2)&(1)/(2)\end{array}\right]`

This tells you the angle of rotation is ...

`tan(\theta)=(sin(\theta))/(cos(\theta))=(\left((√(3))/(2)\right))/(\left((1)/(2)\right))=√(3)\\\\\theta=\arctan{√(3)}=60^(\circ)`

The angle of rotation is 60°.