# Alternate angle for sin (2*theta) ?

1. Sep 5, 2006

### coconutgt

I believe this could be the easiest math post of the day, but it's been too long for me to recall. Anyways, I'm working on the problem where I have to find 2 alternate angles. I got the first (smaller) angle right which is sin(2*theta). Now I have to find the second (bigger) angle which is suppose to involve pi with the sin(2*theta) in some way. Thanks :)

2. Sep 5, 2006

### Staff: Mentor

Can you post a sketch or something? Does the term "alternate" angle mean something significant in the problem? I'm not sure you've given enough info for us to be able to help you.

3. Sep 5, 2006

### Office_Shredder

Staff Emeritus
sin(2*theta) isn't an angle.

Although you may be looking for pi-2*theta, a better description of the problem would be good

4. Sep 5, 2006

### coconutgt

The drawing shows an exaggerated view of a rifle that has been ‘sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v0 = 576 m/s, there are the two possible angles 1 and 2 between the rifle barrel and the horizontal such that the bullet will hit the target. One of these angles is so large that it is never used in target shooting. Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identity may be useful: 2 sin cos = sin 2.)

Pic: http://i96.photobucket.com/albums/l182/coconutgt/rifle.gif

I worked out and got the (a) part which is:

sin(2*theta) = (g*x)/(v0)^2

---substitute everything

sin(2*theta) = (9.8*91.4)/(576)^2

---then

theta = 1/2 * sin^-1[(9.8*91.4)/(576)^2]

theta = 0.07734 degree

5. Sep 5, 2006

### coconutgt

I got it. What I did was graph the sin(2*theta). I then got 2 points from the graph which are:

45 degree - x = 0.07734 degree
45 degree + x = 89.92266 degree <--- (b) answer

So, the alternate angle is just 90 degree (pi/2) - the first smaller angle which came from the original sin(2*theta)

:D

6. Sep 5, 2006

### Staff: Mentor

Good job coconutgt. Welcome to PF, BTW. As you can probably tell, a clear problem statement helps us to help you in one or two replys at most. Mixed or partial problem statements make it a lot harder to help you with hints or error corrections quickly. PF is a great, diverse place.