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The voltage of two alternating electrical currents are given by V0=3sin(ωt) and V1=8sin(ωt+120°).
The voltages add to give a total of Vsin(ωt+θ).
Find V and θ.
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Raymond is riding a ferris wheel. His height h meters above the ground t seconds after the ride starts is given by h(t)=asin(bt+c)+24, where a,b>0 and −π≤c≤π.
The ferris wheel makes a full revolution in 2 minutes.
Show that b=60π.
Raymond reaches a maximum height of 45 meters for the first time after 50 seconds.
Find the value of
a
c
Determine the length of time between when Raymond is first at his lowest point and when he first returns to his starting point.
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Consider the function g(x)=asinbx+c for 0≤x≤24. The graph of g is shown in the diagram below.
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The x-intercepts are q and r, and the point P lies at the minimum.
Find the coordinates of P.
Find the value of q and the value of r.
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