MHB Phasor to sinusoid conversion help

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To convert the phasor V = 169∠-45° at a frequency of 60Hz to a sinusoidal function, the angular frequency is calculated using the formula ω = 2πf, resulting in ω = 2π(60) = 377 rad/s. The sinusoidal representation is then expressed as 169cos(377t - 45°) V. The distinction between frequency in Hz and angular frequency in rad/s is crucial, as they are measured in different units. Understanding this conversion is essential for accurate waveform representation. The discussion emphasizes the importance of recognizing the relationship between frequency and angular frequency in electrical engineering.
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Convert the following phasor to sinusoid:

V = 169\angle-45degrees where f = 60Hz

The answer given is 169cos(377t - 45degrees) V

I am sure I am missing something, but how does the frequency go from 60 to 377?
 
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You just multiply by 2(pi). :)
 
A little bit more detail, to expand on dstorm's post:

$$\omega = 2\pi f,$$
where $\omega$ is the angular frequency (that shows up multiplying $t$ in the waveform), and $f$ is just the frequency. Typically, the units will be a tip-off: $f$ is usually measured in Hz, whereas $\omega$ is usually measured in rad/s.
 
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