Question

The question is in the picture a)Find I when t=0.14 s b) graph the function

Answer 1

1) Let's plug into that function, the entry t=0.14

`\begin{gathered} I=150\sin (60\pi\cdot0.14) \\ I=150\sin ((42)/(5)\pi)\Rightarrow\sin \text{ (2}\pi*4+(2)/(5)\pi)\Rightarrow\sin ((42)/(5)\pi)=\sin ((2)/(5)\pi) \\ I=150*\sin \text{ (}(2\pi)/(5))\Rightarrow(\sin 2x=2\sin (x)\cdot\cos (x) \\ I=150*2\sin ((\pi)/(5))\cdot\cos ((\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{√(2)\left(√(5)+1\right)\sqrt{5-√(5)}}{8} \\ I=150\cdot\frac{√(2)\mleft(√(5)+1\mright)\sqrt{5-√(5)}}{4} \\ I\approx285.32 \end{gathered}`

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: