Unit Circle Calculus

Question

Suppose the minute hand of an analog watch is exactly 1 inch long, and that the number 12 is located at (0,1), 3 is located at (1,0), 6 is located at (0,-1), and 9 is located at (-1,0). (F - TF.A.2) 

1. What are the coordinates of the tip of the minute hand 22.5 minutes after midnight? 
2. The coordinates along a unit circle are given by (cos(x), sin(x)), where the argument x is measured from the positive x-axis in a counter-clockwise direction. If we want to determine the coordinates of the tip of the minute hand by measuring x from the hand's position at 12 o'clock, in a clockwise direction, what adjustments must be made to the argument of the sine and cosine functions in order to give the correct coordinates?
3. How far from the horizontal axis is the tip of the minute hand 520 minutes after midnight? Explain your reasoning.

Answer 1

1 (r,θ) at 22.5 min after midnight:

using 360º = 60 minutes, 1 minute = 6º

Then 22.5 x 6º = 135º

(1,135º) is the coordinate.

2 You would switch the +,- settings of Quadrant 2 and 4

3 That distance d_y would be Sine(70°) = d_y/1, then d_y = 1xSin(70°) = 0.940