# 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). #### Search Tags

basic, math, puzzle, sine function, trigonometry 