Find out the biggest element in the set { cos1, cos2, cos3 } .

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We need to determine the biggest value among cos1, cos2, and cos3

Since 1 is in the first quadrant, then the cosine is positive, then cos1? 0

However, 2 belongs to the interval (pi/2, pi) =(3.14/2, 3.14)which is in the 2nd quadrant where the cosine is negative ,

then cos2<0

Also, 3  belongs to the interval (pi/2, pi)  where cosine is negative.

Then cos1 is the biggest value.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Because 1 is in the interval (0,pi/2), namely the first quadrant, where the function cosine is positive, then cos 1 > 0.

Because 2 and 3 are in the interval (pi/2, pi), then cos2 and cos 3 < 0, because of the fact that the interval (pi/2, pi) is the second quadrant, where the values of cosine function are negative.

So the biggest element is cos 1.

The calculus have been made using the approximate value of pi=3.1416...

pi/2=3.14/2=1.07..

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find the biggest among cos1 cos2 and cos 3.

cos1 is a ratio of the first quadrant and it is is positive.

cos2 is a ratio in secon quadrant an so it is negative. So cos 2 < cos1.

Cos 3  is also in 2rd quadrant, as 3 < Pi. So it is negative

Cosine is decreasing function in the 2nd quadrant from 0 to -1. So cos3 < cos2.

Thus cos3 <cos2 < cos1

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