By David Machin (auth.)

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**Additional info for Biomathematics: An Introduction**

**Sample text**

Thus sin 2~ = 0. Similarly sin 4rr =sin 6rr = ... = 0. In general sin 2n~ = 0 if n is a positive or negative integer or zero. As we go round and round the circle (anticl6ckwise or clockwise) starting from U, y becomes zero at the end of each rotation. It also becomes zero at each half rotation where 8 = rr, since P and N are now at S and PN = 0, giving sin ~ = 0. As P moves continually round the circle sin 8 = 0 when 8 = ~. 3~, 5~, etc. On the other hand when 8 = rr/2, y = PN takes its maximum value of +a.

It also becomes zero at each half rotation where 8 = rr, since P and N are now at S and PN = 0, giving sin ~ = 0. As P moves continually round the circle sin 8 = 0 when 8 = ~. 3~, 5~, etc. On the other hand when 8 = rr/2, y = PN takes its maximum value of +a. 14 sin 8 sin PN OP TI 2 a a 1 However when 8 = 3~/2, y = -a and consequently sin 8 = sin 3~/l = -1. By following the perpendicular PN, while moving P around the circle, it is clear that sin 8 lies in the range -1 to +1. 6. By similar considerations to those previously described, the graph of cos 8 is the same as that of sin 8 except in that it is shifted along by rr/2.

53 If the probabilities are in the ratio 3:2:1, what are the probabilities of the different types now? Compare your answer with the terms of (P + Q + R) 2 when P = 3/6, Q = 2/6 and R = 1/6. 9. Two morphometric characters x 1 and x 2 of a certain species of ape at:e thought to be related to each other by means of the allometric equation: x 2 = ax 1 S where a and S are constants. Suppose these characters were measured on a young ape on two occasions. The measurements on the first occasion were (x 1 , x 2 ) and on the second occasion these had both increased by amounts E and o, respectively.