Answer
(a) $(3/4,-\sqrt 7/4)$
(b) $(3/4,\sqrt 7/4)$
(c) $(-3/4,\sqrt 7/4)$
(d) $(-3/4,-\sqrt 7/4)$
Work Step by Step
Since both coordinates of the Terminal Point of $t$ are positive, $t$ is in Quadrant I.
Therefore, $-t$ is in Quadrant IV.
Adding or subtracting $\pi$ from t or -t moves it by 2 Quadrants.
(a) $-t$
Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative: Terminal Point = $(3/4,-\sqrt 7/4)$
(b) $4\pi + t = t + 4\pi$
Starting in Quadrant I (t), and moving 8 Quadrants $(+ 4\pi)$, we reach Quadrant I. Therefore, the x-coordinate is positive and the y-coordinate is also positive. Terminal Point = $(3/4,\sqrt 7/4)$
(c) $\pi -t = -t + \pi$
Starting in Quadrant IV (-t), and moving 2 Quadrants $(+\pi)$, we reach Quadrant II. Thus, the x-coordinate is negative, and the y-coordinate is positive. Terminal Point = $(-3/4,\sqrt 7/4)$
(d) $t - \pi$
Starting in Quadrant I (t), and moving 2 Quadrants $(- \pi)$, we reach Quadrant III. Therefore, the x-coordinate is negative, and the y-coordinate is also negative. Terminal Point = $(-3/4,-\sqrt 7/4)$
