# What method should be used to determine when a function is zero when using a plotted graph?

I have a function $l(t) = 220 \sin(30 \pi t + \pi/6)$. I have plotted the function using the plot method.

I now have to find out when the current (l) equals zero. Having plotted the function, how do I use Mathematica to tell me when the current (l) equals zero?

The current (l) is the y-axis and time(t) is the x-axis.

For reference, the plotted function looks like this:

• Solve[220 Sin[30 π t + π/6] == 0, t] and hence ${-\pi + 12 \pi k \over 180 \pi}$ for $k$ and integer. Incidentally, never ever use $I$ as a variable, since it is a constant in Mathematica ($I = \sqrt{-1}$). Commented Nov 17, 2016 at 1:08
• Thank you! And yes, I didn't use I as the variable in the code, I used y. Commented Nov 17, 2016 at 1:49
• So... doesn't my answer suffice? Commented Nov 17, 2016 at 1:50
• For this specific Plot you can include a constraint: Solve[{220 Sin[30 Pi x + Pi/6] == 0, 0 <= x <= 2/15}, x] Commented Nov 17, 2016 at 1:50
• @DavidG.Stork Yes it does. I just forgot to mark it as the answer. Thanks again! Commented Nov 17, 2016 at 2:03

Solve[220 Sin[30 π t + π/6] == 0, t]


I post this just to illustrate:

• how to utilize solutions (and specify range)
• use of Mesh andMeshFunctions to visualize zeroes

func[t_] := 220 Sin[30 Pi t + Pi/6]
With[{roots = t /. Solve[{func[t] == 0, 0 < t < 2/15}, t]},
Plot[func[t], {t, 0, 2/15}, Mesh -> {{0}}, MeshFunctions -> (#2 &),
MeshStyle -> Directive[Red, PointSize[0.02]],
Epilog -> {Arrow[{{#, 150}, {#, 0}}] & /@ roots,
Text[Framed[#], {#, 150}, {0, -1}] & /@ roots}, Frame -> True]]