Hello

The only linear functions mapping into are for hence the problem boils down to finding a constant such that for .

Since for , the sine function is a concave function on this interval thus the line which passes through the points and is under the curve of . In other words, as long as .

If you don't know what a concave function is, you can show that is non negative on .

Hint : show that and that g is increasing on and decreasing on .

Note : choosing is useful (compulsory !) if one uses the fact that is a concave function. If one uses the second method, can be any real number which lies in .