Getting a triangle from trigonometric function

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Discussion Overview

The discussion revolves around how to derive the dimensions of a right triangle using trigonometric functions, particularly focusing on the relationships between angles and side lengths. Participants explore the implications of defining one side of the triangle based on the sine function and seek clarification on how to express the other sides and angles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant asks how to derive all triangle values from trigonometric functions, specifically using sin(x) = y.
  • Another participant suggests setting the hypotenuse to 1 to simplify calculations and asks what the opposite side would be in that case.
  • There is a request for a clearer format to express the triangle's dimensions, specifically asking for labels like hyp =, a =, b =.
  • Participants discuss the angles in the triangle, noting that if one angle is x and there is a right angle, the third angle would be 90 - x.
  • One participant references a diagram provided by another to help visualize the relationships between the sides and angles.

Areas of Agreement / Disagreement

Participants generally agree on the basic relationships in a right triangle as defined by trigonometric functions, but there is no consensus on the best way to express or derive all necessary values, as some seek clarification while others provide different approaches.

Contextual Notes

Some participants express confusion regarding the format for presenting triangle dimensions, indicating potential limitations in communication or understanding of the relationships involved.

Who May Find This Useful

This discussion may be useful for students learning about trigonometric functions and their applications in geometry, particularly in understanding the relationships between angles and side lengths in right triangles.

enter
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How can I get a right triangle from the inputs and outputs of trigonometric functions?
For example: sin(x) = y
The triangle would have one angle as x and the opposite edge of the triangle would be y/hyp etc.
How can I get all of these values from any trigonometric function?
Please tell me if I am missing some needed values and if I need extra inputs.
Thank you in advance.
 
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Since the sin(x) is a ratio of sides y/hypotenuse, you can pick the value of one side say the hypotenuse to be 1 and the side opposite the angle x is what?

So now you have two sides of a right triangle what does that suggest to get the third side?

This is the most basic way to solve it, however there are other ways to solve this using trig identities too.
 
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I don't understand, can you format this like:
hyp =
a =
b =
?
 
Okay, draw a right triangle. You know angle x and you know there's a 90 degree angle too.

so what is the third angle in terms of x?
 
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enter said:
I don't understand, can you format this like:
hyp =
a =
b =
?

Use this diagram:

trigfunc.gif
Set the length of the hypotenuse, c = 1

sin θ = b then. What is a?
 
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jedishrfu said:
Okay, draw a right triangle. You know angle x and you know there's a 90 degree angle too.

so what is the third angle in terms of x?
90-x?
 
yes now follow @SteamKing 's diagram and you should be able to work out the other trig function values.
 
Ok, thank you!
 

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