Jyā, koti-jyā and utkrama-jyā

Jyā, koti-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematicians and astronomers. The earliest known Indian treatise containing references to these functions is Surya Siddhanta. These are functions of arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine. In fact, the origins of the modern terms of "sine" and "cosine" have been traced back to the Sanskrit words jyā and koti-jyā.

Definition

Let 'arc AB' denote an arc whose two extremities are A and B of a circle with center O. If a perpendicular BM be dropped from B to OA, then:

If the radius of the circle is R and the length of arc AB is s, the angle subtended by arc AB at O measured in radians is θ = s / R. The three Indian functions are related to modern trigonometric functions as follows:

KOJY

KOJY (106.9 FM) is a commercial radio station that serves the Bloomfield, Iowa and Ottumwa, Iowa area. The station broadcasts a Southern Gospel format. KOJY is licensed to Mark and Karen McVey, through licensee Tri-Rivers Broadcasting Company. KOJY simulcasts the Southern Gospel format "God's Country" with 89.7 KVCI in Montezuma, Iowa. The station formerly simulcasted a classic hits format with KMEM-FM in Memphis, Missouri as "Mustang" until KDMU switched back to a Gospel format and changed call signs back to KOJY.

The station was originally licensed as KXOF on June 21, 1982 but changed callsigns to KOJY on July 6, 2002 and to KDMU on February 27, 2006, only to change back to KOJY on July 14, 2009.

The transmitter and broadcast tower are located 2 miles northeast of Bloomfield along U.S. Route 63. According to the Antenna Structure Registration database, the tower is 104 m (341 ft) tall with the FM broadcast antenna mounted at the 101 m (331 ft) level. The calculated Height Above Average Terrain is 112 m (367 ft).