Page 90 - Math SL HB Sem 1

CIRCULAR FUNCTIONS AND TRIGONOMETRY

DEFINITION OF TRIGONOMETRIC RATIOS IN TERMS OF THE UNIT
CICLE

Let the point P (x,y) be a point on the circumference of the unit circle,
x" + y'= I with the centre of the origin (0,0) and radius I unit
vl

P(x J)
v
-rM

MP
sln 6r: __ v figure 7
OP

cos A: MO
OP

In the first quadrant we extend Op to rneet the
tangent at A(1,0) so that it meets this tangent at e.
Q's position rclative to A is defined as the tangent
function
AQ NP AQ sind
l.e
OA ON I cos d
v
Q(1,lan0)

tan0
sin0

N A( r, 0)
cosd

figurc 8
Therefore, 1r,r9= i'n{

+-o