Mathematics in Ancient and Medieval India c8.40

c8.40

The R Sine of the *bhūja* is defined to be the R Sine of the corresponding anomaly and the R Sine of the *koṭi* is defined to be the R Cosine of the corresponding anomaly. The R Sine is positive in the first and second quadrants and negative in the third and fourth quadrants. The R cosine is positive in the first and fourth quadrants and negative in the second and third quadrants. Then we have, $R Sin AP₁ = P₁E R Cos AP₁ = P₁F$ $R Sin AP₂ = P₂H R Cos AP₂ = -P₂G$ $R Sin AP₃ = -P₃M R Cos AP₃ = -P₃N$ $R Sin AP₄ = -P₄S R Cos AP₄ = PT₄$ This is equivalent to $R Sin (90⁰ + A) = R Sin (90⁰ - A) = R Cos A$ $R Sin (180⁰ + A) = -R Sin A$ $R Sin (270⁰ + A) = -R Sin (90′ - A) = -R Cos A$ $Where A < 90⁰$ Similarly R Cosine formulae can also be deduced.