I'm trying to help someone with Physics and I need help with differentiation.?

I have β = arcsin(b/c) where b = (15-50*t) and c is constant. So

β = arcsin((15-50*t)/c)

I need an expression for dβ/dt, the rate of change of angle β.

2012-07-25T15:05:03Z

I appreciate what He Who ... said. OK I see how He Who got that. I plugged in 0.6 s for time and I get 2.36 for the rate at that time. That seemed to low for the context. Perhaps because I was assuming units of degrees/s. Now it occurs to me that might be in radians/sec. What determines which it is? Maybe it's always radians?

He_Who_Shall_Not_Be_Named2012-07-25T14:24:46Z

Favorite Answer

Abuse chain rule...
d/dx( arcsin(x) ) = 1 / sqrt( 1 - x^2 )

dβ/dt = 1 / sqrt( 1 - ( (15-50t)/c )^2 ) * -50/c

(Edit) Additional Details:
Choosing degrees or radians typically depends on the problem, not on the equation. I believe in this case, radians are the correct usage.
sin(β) = b/c
b = b(t) which has units of seconds. I assume that the constant c also has units of seconds. If this is the case, the units cancel and you are left with a unit-less value (aka radians).

10

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