## Other small discoveries

Some other discoveries from Aryabhata were:

- produced definitions of sine, cosine, versine, and inverse sine

- made a table of sines

- principle of inversion which means starting from the solution and working backwards

- concept of decimal values: tens, hundreds, thousands

- simplifying hypotheses

- method for finding celestial latitudes

- examines integer solutions to equations of the form: by = ax+c and by = ax-c (a, b, c are integers)

- values of intervals at 90 degree, he used sin(x+1)x-sin nx

- discovered teh versine = 1 - cosine for trigonometry

- gave formulas for calculating the area of triangles and squares

- produced definitions of sine, cosine, versine, and inverse sine

- made a table of sines

- principle of inversion which means starting from the solution and working backwards

- concept of decimal values: tens, hundreds, thousands

- simplifying hypotheses

- method for finding celestial latitudes

- examines integer solutions to equations of the form: by = ax+c and by = ax-c (a, b, c are integers)

- values of intervals at 90 degree, he used sin(x+1)x-sin nx

- discovered teh versine = 1 - cosine for trigonometry

- gave formulas for calculating the area of triangles and squares