A generator at a regional Power Station produces an alternating voltage, according to the function, 𝑉 below:

𝑉 = 240sin(2𝑡)

An electrical engineer needs to determine when this generator will have a voltage that is exactly +120 V.

i) How many times in the interval 0 ≤ 𝑡 ≤ 2𝜋 will the voltage reach +120 V?

ii) Determine the exact times when this occurs for 0 ≤ 𝑡 ≤ 2𝜋.

I would like the answer to ii) with workings so I can see how it is done, I do not need i) answered.


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  • Erdos Erdos

    Leave a comment if you need any clarifications.

  • Hi Philip, I believe that two of the solutions above produce a negative 120v, where we need the 4 times the voltage is a positive 120. Could you clarify further for me? Thanks!

  • I managed to see from your solution that positive 120 was just occuring pi/12 seconds on the other side of the x intercept to negative 120v. Wouldn't have got there without your help though, thank you!

  • Erdos Erdos

    Hi Kyshogle, I had unconsciously solved the equation 240cos(2t)=120. Sorry about that. Attached is the solution for 240sin (2t)=120. I apologize for any inconvenience this may have caused.

The answer is accepted.
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