A particle starts from on the unit circle and moves counter-clockwise along the…

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

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

. (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. (ii) Using these coordinates, find approximate values of

\sin s

and

\cos s

. (iii) Compute

\sin^{2}\!s+\cos^{2}\!s

with your approximations and comment on how close the result is to

1

. (iv) Give one reason, based on the geometry of the unit circle, why small numerical errors may arise in part (iii).