Yes. Similar idea. Sometimes they would also use minutes. Whether this was as a result of contact with the Greeks I do not know. Indian trigonometry however has a different flavour from the trigonometry of Hipparchus.
What Indian mathematicians typically used was a circle with radius 3438 units. Where units would be one of the standard units of length.
Why 3438 you may wonder.
They also wanted to divide the circle into 360 x 60 minutes. For the standard circle they wanted each of those minute arcs to be of 1 unit length. The radius that would accomplish this is (360 x 60)/ 2pi ~= 3438 units.
An angle of 1 minute would then be described as arc length 1 unit on that standardized circle of radius 3438 units.
Indian version of sine and cosine were not expressed as ratios but the corresponding (half) chord for a hypotenuse of 3438 units.