Rotating Voltage Phasor: Frequency of Sinusoidal Voltage at 3/4 Peak Value

[Deathfish]

Homework Statement

At what frequency does a sinusoidal voltage reach 3/4 of its peak value 2.5ms after the zero crossing?

a) 54 Hz
b) 56 Hz
c) 58 Hz
d) 47 Hz

Homework Equations

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The Attempt at a Solution

$$\frac{3}{4}$$ x 90 = 67.5
2.5ms / 67.5 x 360 = 1/75
Period is 1/75
Therefore Frequency is 75 Hz (?)

 

[tedbradly]

$$3/4 = sin(\theta)\to \theta = arcsin(3/4)$$
then
$$\theta = 2 \pi f t \to f = \frac{\theta}{2 \pi t} = \frac{arccsin(3/4)}{2 \pi 2.5ms} = 54 Hz$$