# Getting a triangle from trigonometric function

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1. Jul 27, 2015

### enter

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.

2. Jul 27, 2015

### Staff: Mentor

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.

3. Jul 27, 2015

### enter

I don't understand, can you format this like:
hyp =
a =
b =
?

4. Jul 27, 2015

### Staff: Mentor

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?

5. Jul 27, 2015

### SteamKing

Staff Emeritus
Use this diagram:

Set the length of the hypotenuse, c = 1

sin θ = b then. What is a?

6. Jul 27, 2015

### enter

90-x?

7. Jul 27, 2015

### Staff: Mentor

yes now follow @SteamKing 's diagram and you should be able to work out the other trig function values.

8. Jul 27, 2015

### enter

Ok, thank you!