Differentiating sin x and cos x: the gradient of one is the next in the cycle
Year 12 Mathematics Advanced · the gradient is measured from the curve, not looked up · x in radians unless you switch · axes x from −2π to 2π, y from −1.5 to 1.5
Start from
Graph
y = sin x tangent marks (x, m) next in cycle
Graph of the current trigonometric function with its tangent at a movable point and marks plotting the measured gradient against x.
Drag the point along the curve, or use the x slider. Press Mark (x, m) to plot the gradient you measured.
π/3
Steps of π/12 (15°), so the special angles are all reachable.
functiony = sin x
point(π/3, 0.87)
gradient m (measured)0.50
next in cycle at xhidden
marks on this curve0
The cycle
Four-step wheel showing sin x, cos x, negative sin x and negative cos x, with the current function highlighted.
Differentiate sin x four times and you are back where you started. Count them.
The degrees trap
Switch to degrees and read the gradient of sin x at x = 0. It is not 1.