A Course of Mathematics, Vol. 2 Of 2: For the Use of Academies, As Well As Private Tuition (Classic Reprint)

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Excerpt from A Course of Mathematics, Vol. 2 of 2: For the Use of Academies, as Well as Private Tuition

When the describing point it has passed over 3, o or half the circumference, and has arrived at A', the sine P M va nishes, or bedomes nothing, as at the point A, and the cosine is again equal to the radius ot the circle. Here the angle son has attained its maximum limit but the radius on may still be supposed to continue its motion, and pass below the diameter aa'. The sine, which will then be Pu, will con. Sequently fall below the diameter, and will augment as u moves along the third quadrant, while onthe contrary er, the cosine, will diminish. In this quadrant too, bath sine and cosine must be considered as negative the former being can contrary side of the diameter, the latter a contrary side of the centre, to what each was respectively in the htat quad rant. At the point B', where the arc is three-fourths of the circumference, or 420, the sine Pu becomes equal to the radius os, and the cosine cv vanishes. Finally, in the fourth quadrant, from a' to A, the sine always below aa', di minishes in its progress, while the cosine which is then found on the same side of the centre as it wasin the first gadtant, augments till it becomes equal to the radius ca.