A particle starts from A(1,0) on the unit circle and moves counter-clockwise along the circle covering an arc length s=0.2 (in radians) to reach a point B.
a. (i) Assuming the arc length equals the radian measure of the angle subtended at the centre, estimate the coordinates of B correct to four decimal places.
b. (ii) Using these coordinates, find approximate values of sins and coss.
c. (iii) Compute sin2s+cos2s with your approximations and comment on how close the result is to 1.
d. (iv) Give one reason, based on the geometry of the unit circle, why small numerical errors may arise in part (iii).