Raymond B. answered • 03/07/23
Tutor
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Math, microeconomics or criminal justice
(7,5)
is a point with x=7, y=5
the vector <7,5> has magnitude = sqr(7^2+5^2) = sqr(49+25) = sqr74 and direction = .95 radians
in polar coordinates (7,5) = (sqr74, tan^-1(7/5)) = about (sqr74, 54.46)= about (8.60, 54.46)
= about (8.6, .95) or about (8.6, .3pi) or about (43/5, .3pi)
sqr74 = the hypotenuse of a right triangle with legs 7 and 5
tan^-1(7/5 is the angle whose tangent = the improper fraction 7/5 = 1.4
54.46 degrees = 54.46pi/180 = about .3pi = about .3(3.141593) = about .95 radians = about 95/100= 19/20
in polar coordinates (7,5) = about (43/5, 19/20) where 43/5 =r and 19/20 = the angle in radians
