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

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  $\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right]$

This tells you the angle of rotation is ...

  $\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}$

The angle of rotation is 60°.