document.write( "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.
\n" ); document.write( "y= 2cos(x+2π/3)+3
\n" ); document.write( "Can someone help me to solve this?
\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #693316 by Boreal(15235) $\"\"$ $\"About$

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$\"graph%28300%2C300%2C-8%2C8%2C-1%2C6%2C2%2Acos%28x%2B%282%2Api%2F3%29%29%2B3%29\"$
\n" ); document.write( "At -2*pi/3, the cos () will be at the normal start, so it will be 1.
\n" ); document.write( "The 2 doubles the amplitude to +/- 2 over the baseline.
\n" ); document.write( "The +3 shifts the whole function upward 3 units.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "The minimum will be pi radians later or at pi/3 or about 1, and its value will be 1.
\n" ); document.write( "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.
\n" ); document.write( "It reaches 5 again 2 pi after the start, which is 4 pi/3, or almost 4. \n" ); document.write( "

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