A pendulum of length 10 cm has swung so that theta is the radian measure of the angle formed by the pendulum and a vertical line .Show that the number of centimeters in the vertical height of the end of the pendulum above its lowest position is 20 sin squared 1/2 theta...

Answer 1

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)

Answer 2

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. If h(𝜃) centimeters is the vertical height of the end of the pendulum
above its lowest position, find the instantaneous rate of change of h(𝜃) with respect to 𝜃 when
𝜃 =
1
6
𝜋