Answer
$(a) (-\frac 35,\frac 45)$
$(b) (\frac 35,-\frac 45)$
$(c) (-\frac 35,-\frac 45)$
$(d) (\frac 35,\frac 45)$
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) $\pi - t = -t + \pi$
Starting in Quadrant IV, and moving 2 Quadrants, we reach Quadrant II. Thus, the x-coordinate is negative, and the y-coordinate is positive. Terminal Point = $(-3/5, 4/5)$
(b) $-t$
Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative: Terminal Point = $(3/5,-4/5)$
(c) $t + \pi$
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 = $(-3/5,-4/5)$
(d) $2\pi + t i$
Starting in Quadrant I, and moving 4 Quadrants $(+ 2\pi)$, we reach Quadrant I. Therefore, the x-coordinate is positive and the y-coordinate is also positive. Terminal Point = $(3/5,4/5)$
