C1 W3 Exercise 3

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

How can I find cos(theta) and sin(theta) for the transformation matrix?

To rotate a vector in the plane by an angle of 𝜃 (radians), the matrix related to this transformation is given by:

𝑀=[cos𝜃 −sin𝜃]
[sin𝜃 cos𝜃]

2

Those are known, well-defined functions, right? If you know the value of \theta then np.sin and np.cos will give you the value of the sine and cosine of \theta.

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3

I feel like I understand the transformation matrix, am getting failed tests despite coding using the numpy methods for sin/cosine as above. Is it possible I’m messing up the negative sine from the second vector? I’d be grateful for some input/hints, am willing to share my notebook if that’s helpful.

4

When rotating a vector counterclockwise by an angle θ, the rotation matrix should have a positive sine component. However, if the rotation is clockwise, then the sine component should be negative.

TL;DR:

  • If you’re rotating counterclockwise, both sin(θ) and cos(θ) should be positive.
  • If you’re rotating clockwise, sin(θ) should be negative, while cos(θ) remains positive.

I can take a look at your notebook to provide more specific guidance. Feel free to share it in Private Messages!

5

Thanks for your response. Clearly the whole clockwise/counterclockwise was something a smarter person would’ve picked up on, but I’m wondering how it affects the other values in the transformation matrix. I’ve tried several things ((np.sin(theta) * -1), np.arcsin(theta) that haven’t panned out either, would love some input on the attached at your convenience.

Best,
Tom

{moderator edit - solution code removed}

6

They show you in the instructions what the matrix needs to look like for a simple rotation. The code you wrote is not the same as what they show, right?

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7

Please keep in mind that you cannot share your answers here! However, you can share your answers with mentors in Private Messages (Click on Profile → Message).

Upon reviewing your code, I noticed a minor issue with the transformation matrix T. Your upper-right element of the matrix needs to be adjusted!

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8

Thank you! was wondering that!