Unit 4: Derivatives of sine and cosine
About this unit
Sine's slope is cos x and cosine's slope is −sin x, because a point going round the unit circle at unit speed moves at right angles to its radius, and this holds when angles are in radians.
By the end, you can: Read the slopes of the sine wave to guess its derivative, confirm the slope at 0 is 1 with sin h / h, and see from a point circling the unit circle why (sin)′ = cos and (cos)′ = −sin.
Modules
5 modulesLearn
- Read the slopes off the waveArticle · Sine is flat at its peaks and steepest at its crossings, so its slope graph looks like cosine; sin h / h → 1 (in radians) fixes the steepest slope at exactly 1.Not started
- Round the circleArticle · A point at (cos t, sin t) moves at speed 1 at right angles to its radius, so its velocity is (−sin t, cos t): (sin)′ = cos and (cos)′ = −sin.Not started
- Find the steepest fallExperiment · Drag along the sine wave to where its slope is −1, at x = π, and watch the slope graph trace cosine.Not started
- Sine and cosine slopesReview · Slope of sin is cos, slope of cos is −sin, both in radians, from the shape, the small-angle fact and the circle.Not started