Inverse trigonometric functions used for difference in angle? I was actually solving a physics question in which I got the equation 3/2 (sin i) = sin r. The graph of (r-i) against i has a constant positive slope till 45 degrees value for i. How do I get this result? The only thing I can get from the equation is that sin r - sin i = sin i/2. I don't have much of knowledge about inverse trigonometric functions, would someone please help me understand this in a simple way?

An intuitive way to see this is to get that sin is a monotonically increasing function from 0 to 90 degrees.So in this range that sinr-sini=1/2(sin i) or sinr-sini vs sini has a constant +ve slope.Now the nature of graph remains same if instead of a monotonous function we have only their variable.So the graph of r-i vs i is a straight line with constant +ve slope.But for how long? Obviously as long as 3/2 sin i< 1 or sin i<2/3 the value of i is close to 45 but lesser than that.
