Question

identify the ordered pairs on the unit circle corresponding to each real number (t). write your answer as a simplified fraction, if necessary. part: 0 / 2 part 1 of 2 (a) (t =-\frac{14pi}{3}) corresponds to the point ((x,y)=square).

Explanation:

Step1: Find a coterminal angle

Add \(2k\pi\) (\(k\in\mathbb{Z}\)) to get a positive - angle. Let's add \(6\pi\) (since \(6\pi=\frac{18\pi}{3}\)) to \(t =-\frac{14\pi}{3}\). So \(t=-\frac{14\pi}{3}+ \frac{18\pi}{3}=\frac{4\pi}{3}\).

Step2: Recall the coordinates on the unit - circle

For an angle \(t\) on the unit - circle, the coordinates of the corresponding point \((x,y)\) are given by \(x = \cos t\) and \(y=\sin t\). For \(t=\frac{4\pi}{3}\), we know that \(\cos\frac{4\pi}{3}=-\frac{1}{2}\) and \(\sin\frac{4\pi}{3}=-\frac{\sqrt{3}}{2}\).

Answer:

\((-\frac{1}{2},-\frac{\sqrt{3}}{2})\)