trigo

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahooknowledge/crazyequation/crazyequation9.jpg

參考資料：
my wisdom of maths + result from http://www.wolframalpha.com/input/?i=12a-6sin2a*cosh2b%3D5pi-3%2C12b-6cos2a*sinh2b%3D0

This is not a trigo question. One way to solve it is to use graphical method which give x~1.3.
More precise value can be obtained by numerical method like Newton's method which gives x~1.30899693899575

actually calculator can solve it
by pressing the "sin" and "pi" buttons

12x - 6sin2x = 5pi - 3

12x+3=6sin2x+5pi

12x+3=(0.10453)(2x)+15.708

12x-0.20906x=15.708-3

11.790x=12.708

x=1.0779
(all cor. to 5 sig. fig.)

12x-6sin2x=5pi-3
12x-12sin x cos x=5pi-3
x-sin x cos x=5pi/12 - 3/12
Comparing the like terms:
x=5pi/12=75