# Thread: Find x where sin(x) gives the same result when expressed in radians or degrees.

1. ## Find x where sin(x) gives the same result when expressed in radians or degrees.

The title is pretty much the question, but for more elaboration..:

Define the functions...
f(x) = sinx where x is measured in radiansg(x) = sinx where x is measured in degrees.On the same set of axes, draw the graphs of both f(x) and g(x) for 0≤x≤20. Indicate on your graph the smallest positive solution to the equation f(x) = g(x) and estimate the numerical value of this x.
Subtext:Of course this is an amusing value of x. It has the property that if you ask me for its sine, I don’t have to ask you whether to put my calculator in radian or degree mode. The answer’s the same!This reminds me of the Centigrade and Fahrenheit temperature scales. If you tell me “it’s 40 below” I don’t have to ask you whether you mean C or F.

I don't understand how to find x using a graph.

2. ## Re: Find x where sin(x) gives the same result when expressed in radians or degrees.

I had to blow the sketch up a bit. The red "line" is the sine function using radians and the sine function using degrees is in blue.

-Dan

3. ## Re: Find x where sin(x) gives the same result when expressed in radians or degrees.

Hi Dan ... I think your graph is not quite right. The red line is sin(x) where x is in radians, but the blue line is not sin(x) where x is in degrees. I believe the equation for the blue line should be sin(x *pi/180) so as to convert x in degrees to a radians for the graph. The first two points where the two functions are equal in the range 0<= x <= 20 would be at x=0 and x = 3.088 (approximately).