Unformatted text preview: r,θ ) of P to its rectangular coordinates ( x,y ) is illustrated in Figure 1.5 , from which we see that x = r cos θ y = r sin θ. (1.3) The derivation of Equation ( 1.3 ) from Figure 1.5 requires a pinch of salt: we have drawn θ as an acute angle and x , y , and r as positive. In fact, when y is negative, our triangle has a clockwise angle, which can be interpreted as negative θ . However, as long as r is positive , relation ( 1.3 ) amounts to Euler’s de±nition of the trigonometric functions ( Calculus Deconstructed , p. 86). To interpret Figure 1.5 when r is negative , we move | r | units in the opposite direction along ℓ . Notice that a reversal in the...
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- Fall '08
- Calculus, Euclidean geometry, Polar coordinate system, Rectangular Coordinates