How do you solve the equation #sqrt2sinx1=0# for #360^circ<x<=360^circ#?
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To solve the equation (\sqrt{2}\sin(x)  1 = 0) for (360^\circ \leq x \leq 360^\circ), follow these steps:

Add (1) to both sides of the equation: (\sqrt{2}\sin(x) = 1)

Divide both sides of the equation by (\sqrt{2}): (\sin(x) = \frac{1}{\sqrt{2}})

Find the angles in the specified range where the sine function equals (\frac{1}{\sqrt{2}}), which is (\frac{\pi}{4}) or (45^\circ) and (\frac{5\pi}{4}) or (225^\circ).

Since the range given is in degrees, ensure that the solutions are within the specified range, (360^\circ \leq x \leq 360^\circ).
Therefore, the solutions within the specified range are (x = 45^\circ) and (x = 225^\circ).
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To solve the equation ( \sqrt{2}\sin(x)  1 = 0 ) for ( 360^\circ < x \leq 360^\circ ), first, isolate the sine term. Then, solve for ( x ) by taking the inverse sine of both sides.
( \sqrt{2}\sin(x)  1 = 0 )
Add 1 to both sides:
( \sqrt{2}\sin(x) = 1 )
Divide both sides by ( \sqrt{2} ):
( \sin(x) = \frac{1}{\sqrt{2}} )
Taking the inverse sine of both sides:
( x = \sin^{1}\left(\frac{1}{\sqrt{2}}\right) )
( x = \frac{\pi}{4} ) or ( x = \frac{5\pi}{4} ) (in radians)
Since the sine function is positive in the first and third quadrants, and ( \frac{\pi}{4} ) and ( \frac{5\pi}{4} ) fall within the specified range ( 360^\circ < x \leq 360^\circ ), the solutions are:
( x = \frac{\pi}{4} ) or ( x = \frac{5\pi}{4} )
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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