Consider the function f(a) = 76 sin(4 pi a) + 11. The output quantity of f is me

Question

Consider the function f(a) = 76 sin(4 pi a) + 11. The output quantity of f is measured in millimeters. Match the following expression the argument of sine the radius of the rotation in millimeters the input of f angle measure swept counter-clockwise from 3 o'clock position the vertical distance above the horizontal diameter (measured in millimeters) the minimum value of f the vertical distance above the horizontal diameter (measured in radius lengths) the maximum value of f the amplitude of the graph of f the midline of the graph of f a. -65 b. 4 pi a c. sin(4 pi a) d. 76 sin(4 pi a) + 11 e. 11 f. 76 g. 87 h. a i. 76 sin(4 pi a) j. 4 pi

Explanation / Answer

1)

the argument of sin is 4pia (b)

2) the radius of rotation in mm

comparing with y = r sin theta

r= 76 (f)

3) input to f is a (h)

4) vertical distance above the diameter

here diameter is dc value i.e 11

so vertical distance is max of 76 sin 4pia which is 76

so (f)

5) the minimum value of is when sin4pia is -1

min value=-76+11 = -65 (a)

6) tha max value of f is when sin4pia is 1

max value =76+11 = 87 (g)

7)

the amplitude of graph of f is 11+76sin4pia (d)

8) the mid line of graph of f is line of symmetry

which is 11 (e)

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