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

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) (Show Source): You can put this solution on YOUR website!

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.
RELATED QUESTIONS
For the sinusoidal function below, give its vertical shift, amplitude, phase shift,... (answered by Alan3354)

For the sinusoidal function below, give its vertical shift, amplitude, phase shift,... (answered by Alan3354)

For the sinusoidal function below, give its vertical shift, amplitude, phase shift,... (answered by josmiceli)

find amplitude,period,frequency,phase shift, and vertical shift. than graph two periods... (answered by lwsshak3)

sinusoidal function Graph the function y=3.5sin(5x-80°)+1.5 by applying transformation... (answered by greenestamps)

Sinusoidal Functions Graph the function y=3.5 sin (5x-80°)+1.5 by applying... (answered by greenestamps)

write an equation of the sine function with the given amplitude, period, phase shift,... (answered by lwsshak3)

Write a sine function with the given amplitude, period, phase shift, and vertical shift. (answered by lwsshak3)