I will also mention that no one that I've spoken to so far knows when negative numbers were introduced into the Cartesian Coordinate system. Was it Fermat? Was it Issac Newton? Maybe someone here knows the answer.
I agree that the reference angle is the part that Mr. Kline left out. It isn't mentioned in Euclid, Ptolemy, or even Descartes work. As a matter of fact, no one I've spoken to so far has any idea as to the origin of reference angle. I'm sure no one just went to bed one night, woke up, and...
As I've stated previously, I've used the substitution method for many years. So when I say 68 = 180 - 112, I can also say 68 = 68 because I can substitute the number 68 in the place of the mathematical statement 180 - 112. So when Morris Kline says tan(A) = tan(180 - B), I can agree with that...
The textbook says as follows: An alternative method of describing the slope of a line with respect to the horizontal or x-axis utilizes the angle which the line makes with the axis. This angle of inclination is the counterclockwise angle whose initial side is the x-axis taken in the positive...
Homework Statement On pages 65-66 of Calculus An Intuitive And Physical Approach, Mr. Kline discusses Inclinations of lines. In illustration 3A-7 he uses the substitution method to create a proof. But there is one step that I think he leaves out. He shows the equation tan A = tan(180 - B) =...