1) Let's plug into that function, the entry t=0.14
[tex]\begin{gathered} I=150\sin (60\pi\cdot0.14) \\ I=150\sin (\frac{42}{5}\pi)\Rightarrow\sin \text{ (2}\pi\times4+\frac{2}{5}\pi)\Rightarrow\sin (\frac{42}{5}\pi)=\sin (\frac{2}{5}\pi) \\ I=150\times\sin \text{ (}\frac{2\pi}{5})\Rightarrow(\sin 2x=2\sin (x)\cdot\cos (x) \\ I=150\times2\sin (\frac{\pi}{5})\cdot\cos (\frac{\pi}{5}) \\ I=150\cdot2\cdot\frac{\sqrt[]{\frac{5-\sqrt[]{5}}{2}}}{2}\cdot\frac{\sqrt[]{5}+1}{4} \\ I=150\cdot2\cdot\frac{\sqrt{2}\left(\sqrt{5}+1\right)\sqrt{5-\sqrt{5}}}{8} \\ I=150\cdot\frac{\sqrt{2}\mleft(\sqrt{5}+1\mright)\sqrt{5-\sqrt{5}}}{4} \\ I\approx285.32 \end{gathered}[/tex]
Note that we had to use trig identity =sin2x=2xsin(x)*cos(x) and the periodicity of that sine function y= sin (2pi x 4 +2/5pi)
2) Plotting that function we have:
