Solving Equation Problem: Power Generated by 240V and 12A

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of power generated by a voltage of 240V and a current of 12A, specifically using the formula P=VIcos(ø-ø). Participants are attempting to reconcile their calculations with the expected answer and are exploring potential errors in their understanding of trigonometric values.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • The original poster (OP) calculates power as 240x12cos(15°-75°) = 1440W but is confused about the intermediate steps leading to this answer.
  • Some participants question the value of cos(60°), with one asserting it should equal 0.5, while another suggests it might be 0.58 due to calculator settings.
  • There is a suggestion that the OP's calculator may be in GRAD mode, which would yield cos(60 grad) = 0.588, potentially explaining the discrepancy.
  • Participants express uncertainty about the correct cosine value and the implications for the power calculation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct value of cos(60°) or the implications for the power calculation. There are competing views regarding the calculator settings and their impact on the results.

Contextual Notes

There is uncertainty regarding the calculator modes (degree vs. grad) and how this affects the trigonometric calculations. The discussion does not resolve the mathematical steps or assumptions made by the participants.

brenfox
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Homework Statement



Determine the power generated by a voltage V = 240∠15° volts driving a current I = 12 ∠75°

Homework Equations



P=VIcos(ø-ø)

The Attempt at a Solution

This is a worked example from my open university course. The answer is 240x12cos(15°-75°) = 1440W. I can not for the life in me work out how they have arrived at this answer. I get cos-60= 0.58. then times 240x12= 1692.9 W. Must be doing something wrong!
 
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How is cos(60°) equal to 0.58?
 
gneill said:
How is cos(60°) equal to 0.58?

It is possible that the OP has their calculator in GRAD mode, since cos(60 grad) = 0.588.

But really one shouldn't need a calculator to calculate cos(60°) = 0.5.
 
Not sure. After inputting cos 60 it came out with 0.58. I am of the understanding cosine 60 equals half. so 240x12x0.5 does equal 1440 Watts . But cosine 60 equates to 0.58 in my calculator.
 
brenfox said:
Not sure. After inputting cos 60 it came out with 0.58. I am of the understanding cosine 60 equals half. so 240x12x0.5 does equal 1440 Watts . But cosine 60 equates to 0.58 in my calculator.

As pasmith indicated, check to make sure that your calculator is in degree mode for angles, not grad mode.
 
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