When a pendulum of length 10 cm has swung so that 𝜃 is the radian measure of the angle formed by the pendulum and a vertical line, then if ℎ(𝜃) cm is the vertical height of the end of the pendulum above its lowest position, ℎ(𝜃) = 20 𝑠𝑖𝑛^2 𝜃/2 . Find the instantaneous rate of change of ℎ(𝜃) with respect to 𝜃 when (a) 𝜃 = 𝜋/3 and (b) 𝜃 = 𝜋/2
h = L (1-cos T) geometry exact
cos 2A = 1 - 2 sin^2 A identity
so
cos T = 1 - 2 sin^2 (T/2)
h = L [ 1 - (1 -2 sin^2 (T/2) ]
= L [2 sin^2 (T/2) ]
= 20 sin^2 (T/2)
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