1. A M

    “If such an angle is between -π/2 and π/2, the cosine is non-negative, otherwise is non-positive”

    Honestly, why do that? What is wrong with saying, “The cosine is positive, otherwise it is negative.” This tendency to sacrifice clarity for unnecessary complication is so bewildering to me in articles like this. Your post is great and very helpful, aiming to be a simple introduction to a very complex topic for many. Be confident that you are explaining it well. You don’t need to sound like other pretentious and write ridiculous things like that. (Really, your post was great otherwise!)

    • I agree with you when there’s an extra (useless complexity), but, non-negative doesn’t mean positive as well as non-positive doesn’t mean negative. Non-negative/positive means >= 0 (or <= 0). If I had written positive and negative, what about the points lying on the line (where the cosine is null)? Unfortunately, it can seem conter-intuitive, but this is the correct mathematical terminology.
      Thank you for the comment!

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