Solving for Theta: Help With a Ballistics Equation

In summary, the conversation was about solving for theta in a ballistics equation, with the person asking for help due to their rusty trigonometry skills. They were given an equation with cos(theta)*sin(theta) on both sides and were unsure how to proceed. Another person clarified that cos(t)sin(t) can be simplified to sin(2t)/2, allowing them to use arcsine to solve for theta. The conversation ended with the person thanking for the help.
  • #1
VantagePoint72
821
34
Hey everyone,
I'm trying to solve for theta in a derivitive of a ballistics equation and I'm afraid I'm stuck. My trigonometry is a little rusty, can someone help me out? I have:

cos(theta)*sin(theta)=gd/2v^2

With the information I'm given I can solve the the right side of the equation ending up with:

cos(theta)*sin(theta)=some number

How do I get theta by knowing what cos(theta)*sin(theta) equals?

Thanks!
 
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  • #2
cos(t)sin(t) = 2sin(t)cos(t)/2 = sin(2t)/2. Now you can use arcsine...
 
  • #3
Just clarifying what Muzza wrote above...so there's no room for misunderstanding :

[tex]cos(t)sin(t) = \frac {2sin(t)cos(t)}{2} = \frac {sin(2t)}{2}. [/tex]
 
  • #4
OK, thanks for the help!
 

1. What is the purpose of solving for theta in a ballistics equation?

The variable theta in a ballistics equation represents the angle at which the projectile is launched. Solving for theta allows us to determine the optimal angle for the projectile to achieve maximum distance or accuracy.

2. How do you solve for theta in a ballistics equation?

To solve for theta, you will need to know the initial velocity of the projectile, the angle of elevation, and the acceleration due to gravity. Use the formula theta = tan^-1((vy/vx) - (1/2)g(x/vx)^2) to calculate the angle at which the projectile should be launched.

3. What are the units of measurement for theta in a ballistics equation?

The units of measurement for theta in a ballistics equation are in radians. However, it can also be converted to degrees by multiplying the value in radians by 180/π.

4. Can you use the same method to solve for theta for all types of projectiles?

Yes, the same method can be used to solve for theta for all types of projectiles, as long as the initial velocity, angle of elevation, and acceleration due to gravity are known.

5. What factors can affect the accuracy of solving for theta in a ballistics equation?

The accuracy of solving for theta in a ballistics equation can be affected by factors such as air resistance, wind speed, and the shape and weight of the projectile. These factors can alter the trajectory of the projectile, resulting in a different optimal angle for maximum distance or accuracy.

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