If #cos(t)=4/7# and #t# is in the 4th quadrant, find #sin(t)#?
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If ( \cos(t) = \frac{4}{7} ) and ( t ) is in the fourth quadrant, you can use the trigonometric identity ( \sin^2(t) + \cos^2(t) = 1 ) to find ( \sin(t) ).
Given ( \cos(t) = \frac{4}{7} ), use the identity to find ( \sin(t) ):
[ \sin^2(t) + \left(\frac{4}{7}\right)^2 = 1 ]
[ \sin^2(t) + \frac{16}{49} = 1 ]
[ \sin^2(t) = 1 - \frac{16}{49} ]
[ \sin^2(t) = \frac{49}{49} - \frac{16}{49} ]
[ \sin^2(t) = \frac{33}{49} ]
[ \sin(t) = \sqrt{\frac{33}{49}} ]
Since ( t ) is in the fourth quadrant, where ( \sin(t) < 0 ), the sine value will be negative.
Therefore, ( \sin(t) = -\sqrt{\frac{33}{49}} ), which simplifies to ( \sin(t) = -\frac{\sqrt{33}}{7} ).
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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.
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.
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.
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.
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