   Question Answers

# In the 5th century, who created the table of chords with increasing $1$ degree ?(A)Hipparchus(B)William Rowan Hamilton(C)Euclid(D)Ptolemy

Hint: A chord of a circle is a line segment whose end-points are on the circle. Ptolemy used a circle whose diameter is $120.$. The table of chords with increasing $1$ degree was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy.
The table of chords with increasing $1$ degree was created by the Greek astronomer, geometer and geographer Ptolemy in the 5th century. Ptolemy constructed a more complete table of chords. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging from $\dfrac{1}{2}$ to $180$ by increment of $\dfrac{1}{2}$. As $\theta$ goes from $0$ to $180$, the chord of ${\theta ^\circ }$ arc goes from $0$ to $120$. It also includes aids for interpolating chords for minutes of angle. Ptolemy used a different large fixed radius than Hipparchus. The advantage of a large radius is that fractions can be avoided. In contrast, our present day trigonometric functions are based on a unit circle, that is, a circle of radius $1$.
Note: Hipparchus produced the first trigonometric table for use in astronomy. It was a table of chords for angles in a circle of large fixed radius. Incidentally, his table was not in terms of degrees, but “steps”, each step being $\dfrac{1}{{24}}$ of a circle.