When does x(t) = 5/6·sin(10t - 0.927) equal 5/12?

[jlawson]

Please see the attached file.

When does the graph of x(t)=5/6*sin⁡(10t-0.927) equal 5/12

5/12=5/6*sin⁡(10t-0.927)

One answer, attached, is when the graph goes through the green points but I can't seem to figure out how to calculate the values of the red points.

Any help would be greatly appreciated.

 

[haruspex]

The value of the function arcsin(y) is defined to be the solution of sin(x) = y that lies in the range (-π/2, +π/2]. There is a second solution π-arcsin(y) in the range (+π/2, +π]. This will form the basis of the 'red' points.

 

[jlawson]

Oh, yep, duh.

Thank you very much for your help.