Question

Match List I (Trigonometric Functions in Specific Quadrants) with List II (Resulting Functions):

List I		List II
A.	Prathamapade Gatachapajya	I.	Kotijya
B.	Tritiyapade Gamyachapajya	II.	Bhujajya
C.	\(\text{Trijya} - \text{Bhujajya}\)	III.	Kotyutkramajya
D.	\(\text{Trijya} - \text{Kotijya}\)	IV.	Utkramajya

• A. A-III, B-IV, C-II, D-I
• B. A-IV, B-III, C-I, D-II
• C. A-I, B-II, C-III, D-IV
• D. A-II, B-I, C-IV, D-III

Hint:

"Radius minus Cosine" is ALWAYS Utkramajya. "Radius minus Sine" is ALWAYS its complementary, Kotyutkramajya.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Indian trigonometry uses the concept of 'Gata' (elapsed) and 'Gamya' (remaining) arcs within the quadrants to determine the sine and cosine values. It also defines the Versine (Utkramajya) and the Co-versine.

Step 2: Detailed Matching of Functions:
1. Prathamapade Gatachapajya (A): In the first quadrant, the sine of the elapsed arc is simply the Bhujajya (Sine). (A matches II).
2. Tritiyapade Gamyachapajya (B): In the third quadrant, the remaining arc's sine relates to the complementary function, the Kotijya. (B matches I).
3. Trijya - Bhujajya (C): Radius minus Sine is defined as the Co-versine or Kotyutkramajya. (C matches IV).
4. Trijya - Kotijya (D): Radius minus Cosine is the standard Utkramajya (Versine). (D matches III).

Step 3: Verification:
Sequence: A-II, B-I, C-IV, D-III. This matches Option (4).

Step 4: Final Answer:
The quadrant-based rules allow for the derivation of trigonometric values for any angle between 0 and 360 degrees.