The electromotive force for an electric circuit with a simplified generator is 𝐸(𝑡) 𝑣𝑜𝑙𝑡𝑠 at 𝑡 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, where 𝐸(𝑡) = 50 𝑠𝑖𝑛120𝜋𝑡. Find the instantaneous rate of change of 𝐸(𝑡) with respect to 𝑡 at (a) 0.02 𝑠𝑒𝑐 and (b)0.2 𝑠𝑒c
Rate of change of the function is calculated as it's derivative so in this rate of change would be equal to "E'(t)=(50sin120\\pi t)'=50\\cdot120\\pi\\cdot cos120\\pi t=6000\\pi\\cdot cos(120\\pi t)" . For t=0.02 instantaneous rate of change then is "6000\\pi\\cdot cos(120\\pi \\cdot0.02)=5824.833" and for t=0.2 instantaneous rate of change then is "6000\\pi\\cdot cos(120\\pi \\cdot0.2)=18849.556" .
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