# Multiply a trigonometry function

1. May 3, 2012

Hi,
I have a question I have learn a bit about trigonometry and I came across this formula

angle = 38
length = 120
formula

length * sin( angle )

now I have look around for the understanding about this formula and tested the formula my self

0.29636857870938531739229664984902

120 * sin( 38 )

0.29636857870938531739229664984902

sin( 38 )

And as you can see they both calculate the same number, Why is this and what would be the point in using this formula.

2. May 3, 2012

### chiro

Hey Pin Head and welcome to the forums.

Your figures are not correct. Using a calculator I get the following:

sin(38) = 0.2963686
120 * sin(38) = 35.56423

In terms of what this means, it is a projection of some vector with length given by length projected on to the x-axis. If you replace sin with cos you get the projection onto the y-axis.

3. May 3, 2012

Hi,
You are correct I don't no why my calculator is giving me
0.29636857870938531739229664984902
but when I tested the same equation in java programming,java gives me the answer you gave

sin(38) = 0.2963686
120 * sin(38) = 35.56423

So what would this formula be good for?

4. May 3, 2012

### chiro

Like I said above, it's useful for taking a vector and finding the x and y components of the vector.

Vectors are used in many things including physics. For example we can represent a vector to represent a force like gravity, or even a force on something like an electron.

Lets say we have a vector (a,b) which is a two-dimension vector. We calculate our length to be length = SQRT(a^2 + b^2) where SQRT is the square root function. We also calculate our angle to be angle = tan(b/a).

Now given an angle and a length we can find our x and y components. We do this by using the relationship x = length x sin(angle) and y = length x cos(angle).

This is just one reason and there are many others. But if you think about how all the scientists, engineers, and others work with systems that have vectors, then you will start to see how this is useful.