一條有關極坐標數學題...

A ：30° B　：210°

ＯＡ＝７　ＯＢ＝３

Ｓｉｎｃｅ　ＡＯＢ　ｉｓ　ａ　ｓｔｒｉｇｈｔ　ｌｉｎｅ, line AOB =OA+OB = 3+7 =10

●ＡＯＢ　ｉｓ　ａ　ｓｔｒｉｇｈｔ　ｌｉｎｅ
-Because A and B are 30° above / below x-axis (Draw it)

As 210 = 30 + 180.

So, AB is a straight line. The length of AB is 7 + 3 = 10

A(7，30°) 和B(3，210°)是極坐標平面上的兩點。求AB的長度
Sol
A(7，30°)化成XY平面
(7Cos30度，7Sin30度)
B(3，210°)化成XY平面
(3Cos210度，3Sin210度)
AB^2=(7Cos30度－3Cos210度)^2+(7Sin30度－3Sin210度)^2
=(7Cos30度+3Cos70度)^2+(7Sin30度+3Sin3度)^2
=100Cos^2 30度+100Sin^2 30度
=100
AB=10