Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 2x - sin x = 0
+129514 We don't really need a calculator, here...
Note, sin2x = 2sinxcosx.......so we have....
2sinxcox - sinx = 0 factor out sinx
sinx (2cosx - 1) = 0
So, setting each factor to 0, we have that
sinx = 0 and this happens at 0 radians and pi radians on the interval ....or....
2cosx - 1 = 0 add 1 to both sides
2cosx = 1 divide both sides by 2
cosx = 1/2 and this happens at pi/3 radians and 5pi/3 radians on the interval
[ These solutions are exact values....]
+129514 We don't really need a calculator, here...
Note, sin2x = 2sinxcosx.......so we have....
2sinxcox - sinx = 0 factor out sinx
sinx (2cosx - 1) = 0
So, setting each factor to 0, we have that
sinx = 0 and this happens at 0 radians and pi radians on the interval ....or....
2cosx - 1 = 0 add 1 to both sides
2cosx = 1 divide both sides by 2
cosx = 1/2 and this happens at pi/3 radians and 5pi/3 radians on the interval
[ These solutions are exact values....]
