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To locate we reason as follows. Let P (t) be the ordered pair P(x,y). For every value of 't' the point P(t) is on the unit circle. Therefore, if one of the coordinates of P(t) is known, using x 2 + y2 = 1, we can find the other coordinate (except for sign).

From the plane geometry, P is the midpoint of arc AA' which is equidistant from x and y axes so that x = y (see fig. no. 3)

Construct PM perpendicular to OA. Then, from school geometry OM= 1/2 OA but OA = 1. Therefore OM = (See fig. no. 4)

Hence x = using x2 + y2 = 1

(1/2)2 + y2= 1

The coordinates of and so on, can be obtained without too much difficulty.

Index

5. 1 Circular function
5. 2 Periodic function
5. 3 Even & Odd
5.4 Graphs of Trigonometric Functions
Supplementary Problems

Chapter 6

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