The –coordinate of a point on the unit circle is and lies in the second quadrant.

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

Problem

The

y

–coordinate of a point

Q

on the unit circle is

0.6

and

Q

lies in the second quadrant. (i) Find the

x

–coordinate of

Q

. (ii) Using the coordinates obtained, calculate all six trigonometric ratios of the angle

\alpha

represented by

Q

. (iii) Verify numerically, for this angle, that

1+\cot^{2}\!\alpha=\csc^{2}\!\alpha

. Show every substitution clearly.