Admirer

part 5

the next day

a teacher called xie lian to her room and mu qing also feng xin joined him

they arrived at the upper class 1 a

" i have someone here, he was a math genius and he will taught you for some mathematics.. you guys the worst " the teacher let xie lian to handle

bai wuxiang said " oh? it's the goddess bo-- "

before he finish his sentence hua cheng cover his mouth and hua cheng bumped his head on his desk again

" everyone, wh..what.. n..o wh-where.. " xie lian was struggling

hua cheng look at him and he was sweating, mu qing talk

" lesson2 , 3, 4 , 5 or 6? "

xie lian look at him and he let mu qing to handle and he started writing something on the chalkboard

" ok? lesson 4.. so can everyone tell me what they have learned on their current lesson? " mu qing said

and another voice said
" why not that handsome man talk to us? why you? "

everyone look at him and everyone nodded

" oh the hell? my friend don't fvking know how to talk to many people and even his voice become more tiny and tiny to the point that you guys can't hear him now that i'm here and also this dumbass friend of ours will help him, got some problem?? " mu qing said

everyone didn't utter any words and listen

he xuan stand up and said

" I didn't learn any of our lessons.. the cartesian coordinate system was too hard.. i'm sure i'm not the only one "

" pre-calculus, cartesian coordinate system isn't that hard.. let me explain " xie lian said

he draw a graph first and said
" in mathematical illustration of two- dimensional cartesian coordinate, the first coordinate tradionally called the abscissa is measured along a horizontal axis, oriented from left to right.. " he pointed on some areas at the board and continue " the second coordinate the oridinate is then measured along a vertical axis, usually oriented from bottom to top" and then point at the board again

he glance at everyone and said " the cartesian coordinate system uses a horizontal axis that is called the x-axis and a vertical axis called y-axis, equations for lines in this system will have both the x and y variable " he stop and said " for example, the equation 2x + y = 2 is an example of line in this system, these two axes cross perpendicular to each other "

" a cartesian equation for a curve is equation in terms of x and y only, definition. parametric equations for curve give both x and y as functions of a third variable.. usually t, any questions? " xie lian said

everyone  was stunned including hua cheng ofc... and mu qing said " ANY QUESTIONS? "

" how to solve cartesian coordinate? " bai wuxiang asks

" hm, easy now listen, example what is 12, 195° in cartesian coordinate? "

no one's answer.. xie lian expected this and continue

and write at the board he recite it

" r= 12 and θ = 195°
• X = 12 x cos (195°)
    X = 12 x - 0.9659
    X = 11.59 to 2 decimal places

• Y = 12 x sin(195°)
  Y = 12 x - 0.2588
  Y = - 3.11 to 2 decimal places

so to point is at ( - 11.59, -3.11) which is in quadrant lll " and he continue

" But when converting from Cartesian to Polar coordinates ...

... the calculator can give the wrong value of tan-1

It all depends what Quadrant the point is in! Use this to fix things " as he speak he write something on the blackboard, he continue

" QuadrantValue of tan-1
IUse the calculator value
IIAdd 180° to the calculator value
IIIAdd 180° to the calculator value
IVAdd 360° to the calculator value
polar example 1
Example: P = (−3, 10)
P is in Quadrant II

r = √((−3)2 + 102)
r = √109 = 10.4 to 1 decimal place
θ = tan-1(10/−3)
θ = tan-1(−3.33...)
The calculator value for tan-1(−3.33...) is −73.3°

The rule for Quadrant II is: Add 180° to the calculator value
θ = −73.3° + 180° = 106.7°
So the Polar Coordinates for the point (−3, 10) are (10.4, 106.7°)

polar example 2
Example: Q = (5, −8)
Q is in Quadrant IV

r = √(52 + (−8)2)
r = √89 = 9.4 to 1 decimal place
θ = tan-1(−8/5)
θ = tan-1(−1.6)
The calculator value for tan-1(−1.6) is −58.0°

The rule for Quadrant IV is: Add 360° to the calculator value
θ = −58.0° + 360° = 302.0°
So the Polar Coordinates for the point (5, −8) are (9.4, 302.0°) "

he added " in summary
To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) :

x = r × cos( θ )
y = r × sin( θ )
To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

r = √ ( x2 + y2 )
θ = tan-1 ( y / x )
The value of tan-1( y/x ) may need to be adjusted:

Quadrant I: Use the calculator value
Quadrant II: Add 180°
Quadrant III: Add 180°
Quadrant IV: Add 360° , get it? "

actually no one get it but.. everyone nodded

" our time is up, we will meet again.. and will have quiz tomorrow or next tomorrow " xie lian said

" wait.. how..? " bai wuxiang said

" hm? "

he xuan pulled bai wuxiang back and then he smiled at xie lian.. mu qing drag xie lian back to their room

while the upper class 1 a discussing about how amazing xie lian is