Matrix Algebra 2.0 Help: Solving Questions with Cosine Laws

[saifh]

Hey guys,

So I'm stuck on another question from the previous one that I posted and would absolutely love it if I can get some help regarding how to attempt this. I literally have no clue at how to go by solving it. I have a feeling for question one that the cosine laws might come in handy but I'm not sure..

View attachment 4833

Thanks in advance!

 

[Ackbach]

Let's take part (i). You have a point, which we'll write in polar coordinates as
$$\mathbf{x}=r\begin{bmatrix} \cos(\varphi) \\ \sin(\varphi)\end{bmatrix}.$$
As the problem states, we need to rotate this point through a counter-clockwise angle $\theta$ so as to get the point
$$\mathbf{x}'=r\begin{bmatrix} \cos(\varphi+\theta) \\ \sin(\varphi+\theta)\end{bmatrix}.$$
Does this second expression suggest anything to you?

 

[saifh]

Let's take part (i). You have a point, which we'll write in polar coordinates as
$$\mathbf{x}=r\begin{bmatrix} \cos(\varphi) \\ \sin(\varphi)\end{bmatrix}.$$
As the problem states, we need to rotate this point through a counter-clockwise angle $\theta$ so as to get the point
$$\mathbf{x}'=r\begin{bmatrix} \cos(\varphi+\theta) \\ \sin(\varphi+\theta)\end{bmatrix}.$$
Does this second expression suggest anything to you?

Ahh ok thanks, I will work off that. That does make more sense thanks.

 

[Deveno]

It's so much easier to reflect across one of the axes...hmm, I wonder...could we rotate our line of reflection to an axis, reflect, and rotate back-does that even work?