Question

At 11:55 p.m., Thomas ties a weight to the minute hand of a clock. The clockwise torque applied by the

weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be
modeled by a trigonometric function.
The torque peaks 15 minutes after each whole hour, when the minute hand is pointing directly to the right,
at 3 Nm (Newton metre, the SI unit for torque). The minimum torque of -3 Nm occurs 15 minutes
before each whole hour, when the minute hand is pointing directly to the left.
Find the formula of the trigonometric functid that models the torque applied by the weight t minutes
after Thomas attached the weight. Define the function using radians.
T(t) =(​

Answer 1

T(t) = 3sin((t-5)π/30)

Explanation:

5 minutes after Thomas ties it on, the torque is zero and increasing. So, the sine function is shifted right 5 minutes. The maximum value is 3, so that is the multiplier of the sine function. The period is 60 minutes, so the coefficient of t is (2π/60) = π/30. The function you want is ...

T(t) = 3sin((t-5)π/30)