Who Is Correct in Calculating Sinusoidal Waveform Values?

[Utech]

I was routinely checking a question in an Engineering Maths book as listed below:

The instantaneous value of voltage in an a.c.
circuit at any time t seconds is given by
v = 100 sin(50$$\pi$$t - 0.523) V. Find:
(a) the peak-to-peak voltage, the periodic
time, the frequency and the phase angle
(b) the voltage when t = 0
(c) the voltage when t = 8ms
(d) the times in the first cycle when the voltage
is 60V
(e) the times in the first cycle when the voltage
is =-40V
(f) the first time when the voltage is a maximum.
Sketch the curve for one cycle showing
relevant points. [(a) 200 V, 0.04 s, 25 Hz,
29.97° lagging (b) -49.95V (c) 66.96V
(d) 7.426 ms, 19.23 ms (e) 25.95 ms, 40.71 ms
(f) 13.33 ms]

Questions (d) and (e) are the one of interest to me, I worked those two questions and my answers were as follows:

(d) 7.43 ms, 12.57 ms
(e) 25.95 ms, 34.05 ms

I have highlighted the discrepancies between my answers and the authors answers. Who is correct ? A cursory glance at second answer of part (e) would show an issue as the periodic cycle is 40 ms so how could it fall out of the first cycle. Is there a different way of calculating negative voltages also. Thanks, any detailed explanations / corrections would be appreciated

 

[berkeman]

I was routinely checking a question in an Engineering Maths book as listed below:

The instantaneous value of voltage in an a.c.
circuit at any time t seconds is given by
v = 100 sin(50$$\pi$$t - 0.523) V. Find:
(a) the peak-to-peak voltage, the periodic
time, the frequency and the phase angle
(b) the voltage when t = 0
(c) the voltage when t = 8ms
(d) the times in the first cycle when the voltage
is 60V
(e) the times in the first cycle when the voltage
is =-40V
(f) the first time when the voltage is a maximum.
Sketch the curve for one cycle showing
relevant points. [(a) 200 V, 0.04 s, 25 Hz,
29.97° lagging (b) -49.95V (c) 66.96V
(d) 7.426 ms, 19.23 ms (e) 25.95 ms, 40.71 ms
(f) 13.33 ms]

Questions (d) and (e) are the one of interest to me, I worked those two questions and my answers were as follows:

(d) 7.43 ms, 12.57 ms
(e) 25.95 ms, 34.05 ms

I have highlighted the discrepancies between my answers and the authors answers. Who is correct ? A cursory glance at second answer of part (e) would show an issue as the periodic cycle is 40 ms so how could it fall out of the first cycle. Is there a different way of calculating negative voltages also. Thanks, any detailed explanations / corrections would be appreciated

Welcome to the PF. Could you please show the way you solved the equation for d) and e)? That would be the quickest way for us to check your math.