References: Trig derivatives from geometry

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Calculus, Chapter 4: "Trig Derivatives through geometry"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/derivatives-trig-functions
  Series index: https://www.3blue1brown.com/?topic=calculus
  License: copyright Grant Sanderson; videos published on his site and YouTube
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Watch this next

• Trig Derivatives through geometry (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Watching the point travel around the unit circle while its velocity arrow stays perpendicular to the radius makes the derivatives (-sin x, cos x) something you see rather than memorize, and the link between the circular motion and the wave-shaped graphs is much clearer animated. About ten minutes.

Going deeper

• Essence of Calculus (full series) by 3Blue1Brown. The series this track follows. The previous chapter derived the power rule from growing squares and cubes; the next (Visualizing the chain rule and product rule) handles functions that are multiplied together or nested inside one another.

• Khan Academy: Calculus for a slower, exercise-driven treatment of the derivatives of trigonometric functions, with practice problems and immediate feedback.

Adjacent topics

Where this sits in the track.

• The power rule from geometry (previous lesson). The power rule covered powers of t; sine and cosine are not powers, so they needed their own picture. Same nudge-and-look method, different shape: a point on a circle instead of a growing square.

• Taylor series (final lesson). The small-angle approximation sin(x) ≈ x glimpsed here is the first term of the sine’s Taylor series. The capstone lesson generalizes that move, approximating any function near a point by reading off its derivatives, with sine as a recurring example.