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How can I derive the sin of a angle

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The answer to your equation would be zero, because θ is not a delivative of d/dt.. otherwise if it were d/dθ sinθ, the answer would be cosθ.


in your problem it seems sinθ is not a function of time (if t is time). therefore the derivative of sinθ with respect to t is zero.

but Θ isn't a function ωt?

ω (rad/sec) * t (sec) = Θ (rad)

Because θ is a function of time (t) then d/dt(sin ωt) = ωcosωt.
The derivative of sine is cosine.


in general

if θ = θ(t) then d(sin(θ(t)))/dt is equal to:

(d(θ(t))/dt) × cos (θ(t))

have a nice day

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