Use translations of the base function to sketch one complete

Use translations of the base function to sketch one complete cycle of the function: List the coordinates of the main final five points of your graph. Label and scale the axes. What is the maximum value of the function? What is the minimum value of the function? What is the average value of the function? Use translations of the base function to sketch one complete cycle of the function: y = -3sin (1/2(x + pi)) -1 List the coordinates of the main final five Label and scale the axes. points of your graph What is the maximum value of the function? What is the minimum value of the function? What is the average value of the function?

Solution

y = 4cos(2(x - pi/2)) -1

Period = 2pi/2 = pi

In 1 cycle of pi there are 5 points:

Five points : ( 0 , pi/4 , pi/2 , 3pi/4 , pi )

y = 4cos(2(x - pi/2)) -1 ; ( -5, 4cos(pi/2 - pi) -1 , 4cos(pi -pi)-1 , 4cos(3pi/2 - pi/2) -1 , 4cos(2pi - pi) -1 )

= ( -5 , -1 ,3 ,-5 , -3 )

b ) Maximum value : y = +4 -1 = 3

c) Minium value : y = -4 -1 = -5

d) Avg value : y = (ymax +ymin)/2 = (3 -5)/2 = -1