Provider: JSTOR www.jstor.org Database: JSTOR Content: text/plain; charset="us-ascii" TY - CHAP TI - Remarkable Analogies A2 - Maor, Eli AB -

Consider the unit circle—the circle with center at the orgin and radius 1—whose equation in rectangular coordinates is${x^2} + \;{y^2} = 1$(fig.66). Let$P(x,\;y)$be a point on this circle, and let the angle between the positive$x$-axis and the lineOPbe$\varphi$(measured counterclockwise in radians). Thecircularortrigonometric functions“sine” and “cosine” are defined as the$x$and$y$coordinates ofP:

$x\; = \;{\rm{cos}}\;\varphi {\rm{,}}\quad y\; = \;{\rm{sin}}\;\varphi {\rm{.}}$.

The angle$\varphi$can also be interpreted as twice the area of the circular sectorOPRin figure 66, since this area is given by the formula$A = {r^2}\varphi {\kern 1pt} /{\kern 1pt} 2\; = \;\varphi {\kern 1pt} /{\kern 1pt} 2$, where$r=1$is the radius.

EP - 150 PB - Princeton University Press PY - 1994 SN - 9780691141343 SP - 147 T2 - "e": The Story of a Number UR - www.jstor.org/stable/j.ctt7t8q5.24 Y2 - 2020/08/05/ ER -