Question

According to the properties of the Sine (Jya) and Cosine (Kotijya) in the four quadrants of the celestial circle, identify the correct statements from the following:
A. In the first quadrant, Jya (Sine) is positive.
B. In the second quadrant, Jya is negative.
C. In the third quadrant, Jya is positive.
D. In the fourth quadrant, Jya is negative.
E. In the fourth quadrant, Kotijya (Cosine) is positive.

• A. Only A, B, C
• B. Only B, C, D
• C. Only A, D, E
• D. Only E, A, B

Hint:

Use the "All-Silver-Tea-Cups" mnemonic or simply visualize the circle. Sine (Jya) is about height—it is positive in the top half (1st and 2nd). Cosine (Kotijya) is about width—it is positive in the right half (1st and 4th).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Indian trigonometry (Jya-ganita) operates on a circle where the four quadrants (Padas) are defined by the signs of the horizontal (Koti/Cosine) and vertical (Bhuja/Sine) offsets. This is identical to the modern Cartesian sign convention for trigonometric functions.

Step 2: Detailed Explanation of Signs in Quadrants:
1. First Quadrant ($0^\circ$ to $90^\circ$): Both Bhuja (Sine) and Koti (Cosine) are positive. Statement (A) is TRUE.
2. Second Quadrant ($90^\circ$ to $180^\circ$): The Bhuja (Sine) remains positive (since it is above the horizontal axis), but the Koti (Cosine) becomes negative. Statement (B) claims Jya is negative, which is FALSE.
3. Third Quadrant ($180^\circ$ to $270^\circ$): Both Bhuja (Sine) and Koti (Cosine) are negative. Statement (C) claims Jya is positive, which is FALSE.
4. Fourth Quadrant ($270^\circ$ to $360^\circ$): The Bhuja (Sine) is negative (below the axis), but the Koti (Cosine) is positive (to the right of the vertical axis). Statement (D) is TRUE. Statement (E) is TRUE.

Step 3: Verification with Options:
- Statements A, D, and E are mathematically correct based on spherical geometry and the quadrant system.
- Option (3) correctly lists these three: "Kevalam A, D, E".

Step 4: Final Answer:
The correct set of statements is A (Jya positive in 1st), D (Jya negative in 4th), and E (Kotijya positive in 4th).