What is the Cartesian form of #( 12 , ( - 15pi)/2 ) #?

Answer 1

(0, 12)

Given # r=12# and #theta = -15 pi/2#
#x= r* cos theta# and # y=r* sin theta#
#x=0#
#y=12#
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Answer 2

The Cartesian form of the point ( (12, -\frac{15\pi}{2}) ) in polar coordinates is obtained by converting the polar coordinates to Cartesian coordinates using the formulas:

[ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

where ( r ) is the radius or distance from the origin and ( \theta ) is the angle in radians measured counterclockwise from the positive x-axis.

Given ( r = 12 ) and ( \theta = -\frac{15\pi}{2} ), we have:

[ x = 12 \cos\left(-\frac{15\pi}{2}\right) ] [ y = 12 \sin\left(-\frac{15\pi}{2}\right) ]

Evaluate the trigonometric functions:

[ x = 12 \cos\left(-\frac{15\pi}{2}\right) = 12 \cdot \cos\left(\frac{\pi}{2}\right) = 12 \cdot 0 = 0 ] [ y = 12 \sin\left(-\frac{15\pi}{2}\right) = 12 \cdot \sin\left(\frac{\pi}{2}\right) = 12 \cdot 1 = 12 ]

So, the Cartesian form of the point ( (12, -\frac{15\pi}{2}) ) is ( (0, 12) ).

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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.

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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