Stephen W.

asked • 07/26/23

real life application on a trigonometric function

1) what is the range and domain of the function f(x)=6cos(π/4x)-2

2) Pls help me create a real life application on the function f(x)=6cos(π/4x)-2 with a detailed soultion


Pls help asap thanks in advance

Luke J.

just to clarify because i don't see spaces or parantheses for it, is that pi divided (4 x) or pi/4 times x (pi/4) (x) it will effect the final answer greatly if it's the first of the two
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07/28/23

Andrew D.

tutor
I second Luke's observation. Trying to create a "real life" application of the function if the x is in the denominator would be quite tricky since this would imply that the frequency of the function would increase infinitely as x approaches zero. Similarly, the wavelength would asymptotically approach zero as x goes to zero, giving you unrealistic behavior - for instance, think a metronome ticking faster and faster until it is going infinitely fast (assuming x --> 0). I'm fairly certain you mean f(x) = 6cos(pi x/ 4) - 2.
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08/05/23

1 Expert Answer

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Robert L. answered • 08/05/23

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The Range is [-8, 4] and the Domain is (-inf, inf).


Common real life example for this function could be your height on a Ferris wheel over time. The max height would be 4 and the minimum would be -8 (perhaps it is mostly underground). "x" would be your time variable (minutes, for example) and the pi/4 would relate to the period (8 minutes) of the motion.

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