- #1
Northbysouth
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- 2
Homework Statement
Reduce the Expression:
15sin(wt-45°) + 5cos(wt-30°) + 10cos(wt-120°)
to the form Vmcos(wt+θ)
Homework Equations
The Attempt at a Solution
My theta value at the end isn't coming out right.
My first step was to put make sure each term was in terms of cosine, hence:
15cos(wt-45°-90°) + 5cos(wt-30°) + 10cos(wt-120°)
Which in phasor form is:
15∠-135 + 5∠-30 + 10∠-120
Then I used cos and sin to find the real values and the j values
15cos(-135) + j15sin(-135) + 5cos(-30) + j5sin(-30) + 10cos(-120) + j10sin(-120)
= -11.28 -j21.77
Which in a phasor format is:
24.52∠62.6
24.53 = (11.282+ 21.772)1/2
62.6 = arctan(21.77/11.28)
But apparently the solution is:
24.52∠-117.39°
What am I missing?
Any help would be appreciated. Thank you