MATH HELP!! NEED ANSWERS BY TONIGHT!MATH HELP!! NEED ANSWERS BY TONIGHT! PLEASE RE-READ HERE!   High School - 10th Grade1.Find two other pairs of polar coordinates for EACH of these points? (2,...

MATH HELP!! NEED ANSWERS BY TONIGHT!

MATH HELP!! NEED ANSWERS BY TONIGHT!

PLEASE RE-READ HERE!

 

High School - 10th Grade
1.Find two other pairs of polar coordinates for EACH of these points? (2, 60degrees), (4,165degrees),(3,315degrees),(2, 7/6pi)

2. Anthony’s teacher told the class that a unit circle has a circumference of 2pi . This confuses him because he thought a circle has 360 degrees . Write a detailed explanation that compares degrees to radians. Be as thorough as possible in order to help Anthony understand the connection, including diagrams

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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1. You should notice that the coordinates of all these points are polar coordinates and you need to remember that a given point may be expressed by an infinite number of polar coordinates such that:

`(2, 60^o) = (2, 360^o - 60^o) = (-2, 180^o - 60^o), (-2, 180^o + 60^o)`

Hence,you may express the point `(2, 60^o)`  using the next three pairs of polar coordinates such that: `(2, 300^o) ; (-2 , 120^o) ; (-2 , 240^o).`

`(-4,165^o) = (-4, 360^o - 165^o) = (4, 180^o + 165^o)`

`(-4,165^o) = (-4, 195^o) = (4, 345^o)`

`(-2, 7/6pi) = (-2,pi-pi/6) = (2,pi/6) = (2,2pi-pi/6)`

`(-2, 7/6pi) = (-2,5pi/6) =(2,pi/6) = (2,11pi/6)`

2. The circumference measures 2pi radians or `360^o` , hence `2pi ` radians corresponds to `360^o`  degrees and `pi `  radians corresponds to `180^o` .

Hence, if you need to express `30^o`  in radians, you need to think that you may get 30^o dividing `180^o`  by 6, hence, writing `180^o`  in radians yields: `30^o = pi/6` .

Hence, `pi/2`  radians corresponds to `90^o` , `3pi/2`  radians corresponds to `270^o ` and, adding `pi/2`  to `3pi/2 ` yields `2pi ` radians, meaning `360^o = 270^o + 90^o` .

Considering all the above, `2pi`  is the corresponding value in radians to `360^o` .

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