I need to plot a graph of the following function for values time, $0≤t≤2π$ to $2π$ (radians). $$y=5\sin\left(2t+\frac{π}{6}\right)$$ I need to describe and define the amplitude, periodic time and frequency. Can the formula be put into Excel somehow to plot the graph?
Thanks
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For a sinusoid of the form $y = A\sin\left(Bx \pm C \right) \pm D$, $A$ represents the amplitude, $C$ gives the phase shift (how far it is shifted over to the left or to the right), and we get the period time by the relation $T = 2\pi/B$.
Since $A=5$, the amplitude is $\boxed{5}$. The period time is $T = 2\pi/2 = \boxed{\pi}$. Since it completes one period by $t = \pi$, then it completes two periods by $t = 2\pi$, so its frequency is $\boxed{2}$.
Your function has an amplitude $A=5$, a period $T=\pi$ and a phase shift $\psi=\pi/6$.
You can use a spread sheet to visualize the graph. A simple way is illustrated in the figures.
You can see the formula used in the column $C$, and in $B3$ the formula is simply $=B2+\$A\$2$. Changing the step in $A2$ you can have les or more points in the graph.