# Thread: intersections of 3sin(2x) and y=2

1. ## intersections of 3sin(2x) and y=2

I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.

2. I presume the reply is being changed. Its not what I was expecting. The book I'm using has not taught me to do questions that way.

3. Originally Posted by Stuck Man
I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
I can see no reason to use a double angle formula: y= 3sin(2x)= 2 so sin(2x)= 2/3. Use a calculator to find $2x= sin^{-1}(2/3)$ and then divide by 2. sin(180- x)= sin(x) so to get the other value, subtract the 2x your calculator gives you from 180.

4. I don't think the last part is correct. The second intersection is at 90 - x. There are two more between 180 and 270.

5. The question can be done with the double angle formula with tangent. My book hasn't covered that.

6. Originally Posted by Stuck Man
I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
since $0 < x < 360$

$0 < 2x < 720$

$3\sin(2x) = 2$

$\sin(2x) = \frac{2}{3}$

$2x = \arcsin\left(\frac{2}{3}\right)$

$2x = 180 - \arcsin\left(\frac{2}{3}\right)$

$2x = 360 + \arcsin\left(\frac{2}{3}\right)$

$2x = 540 - \arcsin\left(\frac{2}{3}\right)$

solve for $x$ in all four equations