SOLUTION: Find all real solutions to the equation: 4 sin (2x-pi/3)=0

Algebra ->  Algebra  -> Test  -> Lessons -> SOLUTION: Find all real solutions to the equation: 4 sin (2x-pi/3)=0      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 547735: Find all real solutions to the equation: 4 sin (2x-pi/3)=0
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
4%2Asin%28%282x-pi%29%2F3%29=0
Dividing both sides by 4
sin%28%282x-pi%29%2F3%29=0

Now looking at the y=sin(x) graph we have
graph%28300%2C200%2C+-10%2C10%2C-10%2C10%2Csin%28x%29%29

We can see that the graph has a y value of 0 ever 180 degrees (though it is a bit hard to see as this graph is in radians, this is a known fact) (or 180*k where k is an integer).

So we get (from now on k is an integer)
2x-pi%29%2F3=180k
2x-pi=180%2Ak%2A3
2x-pi=540%2Ak
2x=540%2Ak%2Bpi
x=%28540%2Ak%2Bpi%29%2F2
Hopefully this helps! Let me know if you are unsure still.