(CHALLENGING )Trigonometry / geometry proof

In summary, the conversation is about a proof involving trigonometry and geometry. The goal is to prove that GL is equal to R(THETA) in length. The only information given is that GT extended is a metal sheet balancing and "rocking" on a circular structure with radius R. The conversation includes a hint about the definition of radians and using the marked point G' on the cylinder to show that GT is also R theta. The conversation ends with a request for other possible proofs for the statement.
  • #1
(CHALLENGING!)Trigonometry / geometry proof

Hey guys I've spent a couple hours on this without even coming close. I'm hoping someone here can drop me a hint.

From the above image I need to proof that GL is R(THETA) in length.
The only other information I have is that GT extended is a type of sheet (metal sheet) balancing and "rocking" forward and backward on the circular structure of radius R (cylinder).

Hints or help or links would be of HUGE assistance.

Thanks in advance!
 
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  • #2


Is there anything to prove?
If you have a circle of radius R, then a circular segment with angle theta has length R theta.
That's about the definition of radians (a unit circle goes around 2pi radians, and has circumference 2pi).

If you let G' be the marked point on the cylinder below G (near which the label for c is written), then G'T along the circle has length R theta. Since G is a point on the circle with center T which also goes through G' (as indicated by the circular arc), GT is also R theta.
 
  • #3


Thanks that makes sense. Anyone else have a proof for what was stated above?
 

1. What is a trigonometry/geometry proof?

A trigonometry/geometry proof is a logical argument that uses known facts and properties of trigonometry and geometry to prove the validity of a statement or theorem. It involves showing step-by-step how the given statement is true based on established principles.

2. Why are trigonometry/geometry proofs challenging?

Trigonometry/geometry proofs can be challenging because they require a deep understanding of geometric and trigonometric concepts, as well as the ability to think abstractly and logically. They can also involve a lot of complex calculations and multiple steps, making them time-consuming and difficult to solve.

3. How do I approach a trigonometry/geometry proof?

When approaching a trigonometry/geometry proof, it is important to carefully read and understand the given statement or theorem. Then, try to identify any relevant geometric or trigonometric principles that can be used to prove the statement. Create a step-by-step plan and systematically apply the principles to prove the statement.

4. What strategies can I use to solve a challenging trigonometry/geometry proof?

There are several strategies you can use to solve a challenging trigonometry/geometry proof. These include breaking down the problem into smaller, more manageable parts, drawing diagrams to visualize the problem, and using previously proven theorems or principles to help prove the statement.

5. What resources can I use to improve my skills in solving trigonometry/geometry proofs?

To improve your skills in solving trigonometry/geometry proofs, you can use textbooks, online resources, and practice problems. You can also seek help from a math tutor or join a study group to discuss and solve challenging proofs together.

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