A point lies on the unit circle such that its -coordinate is and the corresponding…

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A point

P

lies on the unit circle such that its

x

-coordinate is

x=-\dfrac{\sqrt3}{2}

and the corresponding angle

\theta

is known to satisfy

\pi<\theta<2\pi

. (i) Find the

y

-coordinate of

P

. (ii) List all angles in the interval

(0,2\pi)

that share the

x

-coordinate

x=-\dfrac{\sqrt3}{2}

. (iii) Identify the value of

\theta

satisfying

\pi<\theta<2\pi

and express it in both radian and degree measure.