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Demonstrate that sin 4 radians < sin 3 radians.  

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yapayapa | Honors

Posted July 25, 2013 at 5:41 PM via web

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Demonstrate that sin 4 radians < sin 3 radians.

 

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aruv | High School Teacher | Valedictorian

Posted July 25, 2013 at 6:00 PM (Answer #1)

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`pi rad=3.14 rad`

`4 rad=(3.14+.86)rad`

`=(pi+.86)rad`

`3rad=(3.14-.14)rad`

`=(pi-.14)rad`

Thus

`sin(4rad)=sin((pi+.86)rad)=-sin(.86rad)`  (i)

`sin(3rad)=sin((pi-.14)rad)=sin(.14rad)`   (ii)

from (i) and (ii)

sin(4rad) < sin(3rad)

because sin(4 rad)<0 and sin(3 rad)>0.

 

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