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A hammer thrower is competing in a track and field meet. He rotates exactly 5 times in 2π seconds, and the motion of his hammer is represented by a sine function.
Which function rule could model this situation?
f(x)=5 sin x
f(x)= sin(5x)
f(x)=5π sin x
f(x)= sin(1/5x)

Respuesta :

Answer:

Therefore the correct option is sin(5x).

Step-by-step explanation:

i) The hammer thrower rotates exactly 5 times in 2[tex]\pi[/tex] seconds.

  Therefore one rotation is completed in [tex]\frac{2\pi }{5}[/tex] seconds.

ii) Since the motion of the hammer is represented by a sine function therefore

  one rotation is considered to be one full cycle and the time period of that cycle

  is given in equation i) and it is T = [tex]\frac{2\pi }{5}[/tex]  seconds.

iii) the equation of a sine function is given by sin(2[tex]\pi[/tex][tex]\frac{1}{T}[/tex]) which in this case would

   be sin(2[tex]\pi[/tex] × [tex]\frac{1}{\frac{2\pi }{5}}[/tex] × x) = sin(5x)

iv) Therefore the answer is sin(5x)

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