# Franklin Kemp

Mathematician
Plano, Texas, USA

(Co)Sine Clock 1 is a 14 inch unit circle wall clock that tells time and trig. It has five hands: second, minute, hour, cosine, and sine. The hour hand is the angle indicator on the unit circle. All cosine sine pairs (the signed lengths of the red hands along x and y axes) appear in half a day. (Co)Sine Clock 2 is a variant of (Co)Sine Clock 1 where the minute hand is the angle indicator so all cosine sine pairs appear in one hour. Replacing the standard hours with 12 fractions of 6.28 = 2*3.14 provides a visual check that half way around the circle from 3 o'clock is 3.14 times the distance from center 0 to 1. This is the definition of pi (~=3.14), the key scale factor for any size circle; namely, C = 2*pi*R.

(Co)Sine Clock 1
35 x 35 x 4 cm
Plastic
2017

A simple math wall clock 2016 Christmas present sparked my looking into the world of math clocks narrowing to a graphical "trig" clock that used cosine and sine to tell time. I realized I could do the reverse: use time to tell trig via the unit circle. On the way I discovered the geometrical fact that a circle whose diameter is the hour hand crosses x and y axes at cosine and sine, respectfully. I modified that gift clock with the proprietary idea of replacing the circle with a disc rotating with the hour hand but under axial slits in the clock face to yield cosine and sine hands. That clock and its refinements run through all cosine sine pairs in half a day. I am the only person in the world to make and have such a clock.

(Co)Sine Clock 2
35 x 35 x 4 cm
Plastic
2017

(Co)Sine Clock 2 is a significant variant of (Co)Sine Clock 1 described above. It departs from the normal analog clock arrangement of minute hand longer than the fatter hour hand. Here the hour hand of (Co)Sine Clock 1 is lengthened to be the large arrow head while the minute hand is shortened and becomes the angle indicator. The circular disc now rotates with the minute hand under the clock face visible through the axial slits to yield cosine and sine hands. The virtue of this clock is that it runs through all cosine sine pairs in one hour. This clock reinforces the observation that one can tell time fairly well with just one hand, the hour hand. I and one other person in the world are the only two who have such a clock.