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is -sin^2(x) <= -1

 Aug 27, 2017

Best Answer 

 #1
avatar+8866 
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-sin2 x  ≤  -1

                       Multiply both sides by  -1  and swap the sign.

 sin2 x  ≥  1

 

The biggest possible value of  sin x  is  1  , and the smallest possible value of  sin x  is  -1  .

So, the biggest possible value of  sin2 x  is  12  or  (-1)2  , which both equal  1  .

There is no way that  sin2 x  can be bigger than  1  .

 

 sin2 x   is not always   ≥  1

 

-sin2 x   is not always   ≤  -1

 Aug 27, 2017
edited by hectictar  Aug 27, 2017
 #1
avatar+8866 
+3
Best Answer

-sin2 x  ≤  -1

                       Multiply both sides by  -1  and swap the sign.

 sin2 x  ≥  1

 

The biggest possible value of  sin x  is  1  , and the smallest possible value of  sin x  is  -1  .

So, the biggest possible value of  sin2 x  is  12  or  (-1)2  , which both equal  1  .

There is no way that  sin2 x  can be bigger than  1  .

 

 sin2 x   is not always   ≥  1

 

-sin2 x   is not always   ≤  -1

hectictar Aug 27, 2017
edited by hectictar  Aug 27, 2017

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