Answer
(a) Reference Number: $\pi/4$
(b) Terminal Point: $(\sqrt 2/ 2, -\sqrt 2/2)$
Work Step by Step
1. Find an angle that has the same terminal point as $-41\pi/4$, and is between 0 and 2$\pi$.
$$-\frac{41\pi}{4} + 6(2\pi) = -\frac{41\pi}{4} + \frac{48\pi}{4} = \frac{7\pi}{4}$$
2. $7\pi/4$ is in Quadrant IV, thus, the Reference Number is given by the equation:
$$t^- = 2\pi - \frac{7\pi}{4} = \frac{8\pi}{4} - \frac{7\pi}{4} = \frac{\pi} 4$$
3. According to the Table 1, the terminal point for $\pi/4$ is $(\sqrt 2/2, \sqrt 2/2)$. In Quadrant IV: x-coordinate is positive and y-coordinate is negative. Therefore, the terminal point is: $(\sqrt 2/ 2, -\sqrt 2/2)$
