Alternate angle for sin (2*theta) ?

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Discussion Overview

The discussion revolves around finding alternate angles related to the expression sin(2*theta) in the context of a physics problem involving projectile motion. Participants explore the mathematical relationships and trigonometric identities relevant to determining these angles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to find two alternate angles related to sin(2*theta), indicating a lack of clarity on the term "alternate" angle.
  • Another participant questions the definition of "alternate" angle and suggests that more information is needed to assist effectively.
  • A third participant clarifies that sin(2*theta) is not an angle and proposes that the larger angle might be expressed as pi - 2*theta.
  • A participant describes a specific physics problem involving a rifle and projectile motion, providing a formula for sin(2*theta) and calculating the smaller angle.
  • Another participant shares their method of graphing sin(2*theta) to find two specific angles, concluding that the larger angle is 90 degrees minus the smaller angle derived from the original equation.
  • A later reply acknowledges the participant's success and emphasizes the importance of a clear problem statement for effective assistance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of "alternate" angle, and there are varying interpretations of how to derive the larger angle from the smaller angle. The discussion remains unresolved regarding the clarity of the problem statement and the terminology used.

Contextual Notes

Some assumptions about the definitions and relationships between angles may be missing, and the discussion relies on the context of a specific physics problem that may not be fully articulated.

coconutgt
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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 :)
 
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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.
 
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
 
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
 
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
 
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.
 

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