solve equation usnig domain (0,2pi). 3sinx-2=5sinx-1

Question

answers in exact form if possible if not round two decimal places.

Answer 1

The trigonometric equation is 3 sin x - 2 = 5 sin x - 1 ,  domain ( 0 , )

3 sin x - 5 sin x  = - 1+ 2

- 2 sin x   =  1

 sin x   =  - 1 / 2

The equation is sin x   =  - 1 / 2  -------->   

The function sin x has a period of , first find all solutions in the using domain ( 0 , ).

The function sin x is negative in third and fourth quadrant.

In thirdquadrant  :

In fourth quadrant : 

   

So the solutions are

Finally, add multiples of to each of these solutions to get the general form.Where n is integer.

The solutions are .