SOLUTION: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points

Algebra ->  Trigonometry-basics -> SOLUTION: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points      Log On


   

Question 1078935: For the sinusoidal function below, give its vertical shift, amplitude, phase shift, period, and range. The, graph two periods of the function, labeling five consecutive key points.
y= 2cos(x+2π/3)+3
Can someone help me to solve this?
Thanks
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
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At -2*pi/3, the cos () will be at the normal start, so it will be 1.
The 2 doubles the amplitude to +/- 2 over the baseline.
The +3 shifts the whole function upward 3 units.
It is the cosine function, twice as high, shifted upward 3, so it goes between 1 and 5, not -1 and 1, and it starts at -2 pi/3, which numerically is a little more than -2 radians, and goes to 4 pi/3, or about 4 radians.
At x=0, it is the cosine of 2pi/3, which is (-1/2), so it will be doubled and added to 3, and the value is 2.
The minimum will be pi radians later or at pi/3 or about 1, and its value will be 1.
It crosses 3 again when the cosine is 0, which occurs at 3 pi/2 normally and here the difference between 3pi/2 and 2pi/3, or 5 pi/6, or between 2.5 and 3.
It reaches 5 again 2 pi after the start, which is 4 pi/3, or almost 4.