How can I rearrange this for the angle?

In summary, the conversation discusses a method for solving for theta using inverse operations and calculating the result for a specific set of values. It also suggests comparing the result to other methods or using intuition to verify its correctness. The conversation also mentions using the inverse sine function to solve for theta and warns about the limitations of this function. Overall, the conversation provides a detailed explanation of how to solve for theta and verify the accuracy of the result.
  • #1
iamBevan
32
0
040e7aedfc5c0a9b37f222e28f99fcdf.png


also - The result I'm getting for d is 18587 - this is when I enter 427 for initial velocity, 45 for theta, and 9.81 for g - is this correct?
 
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  • #2
To rearrange, use inverse operations to move things you don't want to the other side -

You're dividing the RHS by g, so multiply both sides by g
You're multiplying the RHS by v^2 so divide both sides by v^2
Then use the inverse sin function
etc.

To see if it's correct, compare the result to some other method for estimating the same thing, or even just your intuition.
 
  • #3
I get 18586- with decimal part .o345...

To solve for [itex]\theta[/itex], "unpeel" what has been done:
[tex]d= \frac{v^2sin(2\theta)}{g}[/tex]
so, multiplying both sides by g,
[tex]dg= v^2 sin(2\theta)[/itex]
dividing both sides by [itex]v^2[/itex],
[tex]\frac{dg}{v^2}= sin(2\theta)[/tex]
Taking the inverse sine (arcsin) of both sides
(be careful- since sine is not one-to-one there is no "true" inverse- there are an infinite number of angles with the same sine- two between 0 and pi/2- and "arcsin" only gives one of them)
[tex]arcsin\left(\frac{dg}{v^2}\right)= 2\theta[/tex]
and, finally, divide both sides by 2:
[tex]\frac{1}{2}arcsin\left(\frac{dg}{v^2}\right)= \theta[/tex]
 
  • #4
Thanks guys - that was a massive help.
 
  • #5


To rearrange for the angle, theta, in the given equation, we can use the inverse trigonometric function of sine. The equation would be rearranged as follows:

sin(theta) = d / (v0^2 / g)

Where d is the distance, v0 is the initial velocity, and g is the acceleration due to gravity.

To find the angle, we can take the inverse sine of both sides of the equation:

theta = sin^-1 (d / (v0^2 / g))

As for the given result of 18587 when plugging in the values for d, v0, and g, it is not a valid angle. The angle should be in radians or degrees, not a numerical value. Please double-check your calculations to ensure accuracy.
 

1. How do I rearrange an equation to solve for the angle?

To rearrange an equation to solve for the angle, you can use basic algebraic principles such as isolating the variable on one side of the equation and performing the inverse operation. For example, if the equation is A = B * sin(angle), you can divide both sides by B and take the inverse sine function to solve for the angle.

2. What are the most common trigonometric identities used to rearrange equations for angles?

The most commonly used trigonometric identities to rearrange equations for angles are the Pythagorean identities (sin^2(angle) + cos^2(angle) = 1) and the double angle identities (sin(2angle) = 2sin(angle)cos(angle) and cos(2angle) = cos^2(angle) - sin^2(angle)). These identities can help simplify equations and solve for angles.

3. How can I use the unit circle to rearrange equations for angles?

The unit circle is a helpful tool to visualize trigonometric functions and their relationships. You can use the unit circle to find the values of sine, cosine, and tangent for specific angles, which can then be substituted into equations to solve for the angle.

4. Can I use inverse trigonometric functions to rearrange equations for angles?

Yes, inverse trigonometric functions such as arcsine, arccosine, and arctangent can be used to solve for angles in equations. These functions "undo" the trigonometric functions and can help isolate the angle variable.

5. Are there any other methods or techniques to rearrange equations for angles?

Aside from basic algebraic principles and trigonometric identities, there are other methods and techniques that can be used to rearrange equations for angles. These include substitution, factoring, and using the properties of special triangles (such as the 45-45-90 and 30-60-90 triangles). It is important to understand the properties and relationships of trigonometric functions in order to effectively rearrange equations for angles.

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