Determine the angles whose points on the unit circle have –coordinate .

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

Problem

Determine the angles whose points on the unit circle have

x

–coordinate

-\dfrac{\sqrt3}{2}

. (i) List all such angles in the interval

0\leq\theta<2\pi

. (ii) For any one of these angles, compute the remaining five trigonometric ratios exactly. (iii) Verify for your chosen angle that

\sec \theta=\dfrac{1}{\cos \theta}

and comment on the sign of

\sec \theta

in its quadrant.