
by the double angle identity for sine. Move everything to one side and factor out the cosine term.

Now the zero product property tells us that there are two cases where this is true,

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of 

, so 

 where 
![n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}](https://tex.z-dn.net/?f=n%5B%2Ftex%20%5Dis%20any%20integer.%5C%5CMeanwhile%2C%5C%5C%5Btex%5D10%5Csin%20x-3%3D0%5Cimplies%5Csin%20x%3D%5Cdfrac3%7B10%7D)
which occurs twice in the interval 

 for 

 and 

. More generally, if you think of 

 as a point on the unit circle, this occurs whenever 

 also completes a full revolution about the origin. This means for any integer 

, the general solution in this case would be 

 and 

.