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Consider the trigonometric function

Consider the trigonometric function-example-1
User Zanbri
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Answers:

Amplitude = 3

Period = 2

Step-by-step explanation

The highest and lowest points occur when y = 2 and y = -4 respectively. The vertical distance between these points is 6 units (because 2 - (-4) = 2+4 = 6)

Half of this is 6/2 = 3 which is the amplitude. It's the vertical distance from the horizontal midline to either the highest point or the lowest point.

The horizontal distance between (-0.25,2) and (0.75,-4) is |-0.25-0.75| = 1 unit. This represents half of the period. A full period goes from one peak to another adjacent peak. Therefore, the period is 2*1 = 2 units. The sine graph repeats itself every 2 units on the x axis. Notice that the distance between the roots (-0.642,0) and (1.358,0) is 2 units.