Consider the function fa 64sin6 pi a 6 The output quantity

Consider the function f(a) = 64sin(6 pi a) + 6. The output quantity of f is measured in millimeters. Match the following expressions with the appropriate quantities. (You may use an answer more than once or some not at all.) the radius of the rotation in millimeters 6pi a angle measure swept counter-clockwise from 3 o\'clock position a the input of f 64 the argument of sine sin(6 pi a) the minimum value of f 6 the vertical distance above the horizontal diameter (measured in millimeters) 6 pi the vertical distance above the horizontal diameter (measured in radius lengths) 70 the maximum value of f 64 sin(6 pi a) + 6 the amplitude of the graph of f the midline of the graph of f 64sin(6 pi a)

Solution

f(a) = 64sin(6pi*a) + 6

period = 2pi/6pi = 1/3

frequency = 3

amplitude = 64 c)

midline =(70 -58)/2 = 6 e)

argument of sine = 6pia a.)

maximum value = 64 +6 = 70 g.)

minimum value = -64 +6 = -58 i)

input of function f is a b.)

angle measure swept from 3\'0 clock position = 6pi f.)

vertical distance above the horizontal diameter is given by ( in mm) = 64sin(6pia) j)

vertical distance above the horizontal diameter is given by ( in radius lengths) = 64sin(6pia) /64 = sin(6pia) d)