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What is the Cartesian form of #( -6 , ( - 9pi)/2 ) #?

Answer 1

Cameron Alexander

#( 0 , 6 )#

It can be seen from the diagram that the x coordinate of P is #rcos(theta)# and the y coordinate of P is #rsin(theta)#

So:

#x=rcos(theta)#

#y=rsin(theta)#

From example:

#x= -6cos((-9pi)/2)=0#

#y = -6sin((-9pi)/2)=6#

So Cartesian coordinate is:

#( 0 , 6 )#

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Answer 2

Emilia Aguilar

To convert the given point (-6, -9π/2) from polar coordinates to Cartesian coordinates, we use the formulas:

x = r * cos(θ) y = r * sin(θ)

where r is the radius and θ is the angle in radians.

Given that r = -6 and θ = -9π/2, we substitute these values into the formulas:

x = -6 * cos(-9π/2) y = -6 * sin(-9π/2)

Now, we calculate the cosine and sine of -9π/2:

cos(-9π/2) = cos(π/2) = 0 sin(-9π/2) = sin(π/2) = 1

Substitute these values into the formulas:

x = -6 * 0 = 0 y = -6 * 1 = -6

Therefore, the Cartesian form of the point (-6, -9π/2) is (0, -6).

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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.