Page 96 - Math SL HB Sem 1

CIRCULAR FUNCTIONS AND TR]GONOMETRY

THE CIRCULAR FUNCTIONS SIN X, COS X, TAN X

(l) f(9) sind
=

I

The above graph ofthe sine function has the following characteristics:

(a) It is continuous (i.e. it has no sudden changes in position).

The donr ain is

(b) It lics entirely within the range - I < sin O < +l

The range is

(c) The shape ofthe graph from 0 :0 to 0 : 2 zr is repeated for each
complete revolution. Such a {irnction is said to be periodic or cyclic. The width of
the repeating pattem, as measured on the horizontal axis, is called the period.
Thus f(d):sin d is a periodic function with a period of ............,

(d) The maximum value is ..... and the minimum value is .......
A graph of this shape, for obvious reasons, is knovvn as a sine wave
(e) The greatest value of gl is called the amplitude of the sine wave and its
lsin
value is

4-t2