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Using the graphs to find the value of x, is sin x cos x > 1 a true statement?

Answer 1

No #sinxcosx>1# is not a true statement.

As #|sinx|<=1# and #|cosx|<=1# (this is for all angles i.e. for all values of #x#, whatsoever), we cannot have their product #sinxcosx>1#

Further #sinxcosx>1=>2sinxcosx>2# i.e. #sin2x>2#, but we cannot have that.

Graphically, just pick up various values of #x# and plot #x# versus #sinxcosx#. Graph appears as shown below.

graph{sinxcosx [-5, 5, -1.92, 3.08]}

Observe that #sinxcosx# cannot have any value greater than #1/2#,

hence #sinxcosx>1# is not a true statement.

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Answer 2

Emery Adkins

To determine if the statement ( \sin(x) \cos(x) > 1 ) is true, we need to consider the behavior of ( \sin(x) ) and ( \cos(x) ) over the range of ( x ).

Since both ( \sin(x) ) and ( \cos(x) ) have values between -1 and 1 inclusive for all real values of ( x ), the product of ( \sin(x) ) and ( \cos(x) ) can never exceed 1. Therefore, the statement ( \sin(x) \cos(x) > 1 ) is false for all real values of ( x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Using the graphs to find the value of x, is sin x cos x &gt; 1 a true statement?

Using the graphs to find the value of x, is sin x cos x > 1 a true statement?