What is the polar form of #( -27,15 )#?

Answer 1

Cameron Alexander

# ( sqrt954 , 2.63 )#

Use the following formulae that links Cartesian to Polar coordinates.

# • r^2 = x^2 + y^2 #

#• theta = tan^-1 (y/x) #

Here x = - 27 and y = 15 .[ Note also that (-27 , 15 ) is a point in

the 2nd quadrant and so care must be taken to ensure #theta #

is in the 2nd quadrant.]

# r^2 = (-27)^2 + (15)^2 = 729 + 225 = 954 #

# rArr r = sqrt954 #

# theta = tan^-1 (15/-27) =- 0.51 color(black)("radians") #

To find #theta color(black)(" in the 2nd quadrant") #

#theta = ( pi - 0.51 ) =2.63 color(black)(" radians") #

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Answer 2

Christopher Agresta

The polar form of the complex number (-27, 15) is 27∠150°.

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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.