Kenneth S. answered • 11/03/17
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I unveil the mysteries and secrets of trigonometry & you'll love it.
It's traditional to say sin 4o when the argument is in degrees.
sin pi = 0 because without the degree symbol, the argument is assumed to be a Real number (radians).
Familiarity with the graph of f(x) = sin x ought to clear up the behavior of this function. There is no discrepancy in what you mention, except that, as Andy points out, sin 4 is really a bit less than what you quoted.
If you got the value 13/184.5 from a specific triangle, and it was said to represent the sine of a 4o angle, then it is apparent that the angle's measurement was rounded off; if the side measurements quoted in this ratio are EXACT, then the angle has to be 4.02008...degrees.
This is an illustration of the dangers of rounding off. Much more precision can be had by carrying calculations out using the full value of trig functions as given by a calculator.
sin pi = 0 because without the degree symbol, the argument is assumed to be a Real number (radians).
Familiarity with the graph of f(x) = sin x ought to clear up the behavior of this function. There is no discrepancy in what you mention, except that, as Andy points out, sin 4 is really a bit less than what you quoted.
If you got the value 13/184.5 from a specific triangle, and it was said to represent the sine of a 4o angle, then it is apparent that the angle's measurement was rounded off; if the side measurements quoted in this ratio are EXACT, then the angle has to be 4.02008...degrees.
This is an illustration of the dangers of rounding off. Much more precision can be had by carrying calculations out using the full value of trig functions as given by a calculator.
