Multiply a trigonometry function

[Pin Head]

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.

 

[chiro]

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.

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.

 

[Pin Head]

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?

 

[chiro]

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?

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.

 

[CellCoree]

I can explain the purpose and significance of multiplying a trigonometry function. Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles. One of the most commonly used trigonometric functions is the sine function, which is used to calculate the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

In the formula you mentioned, the length is multiplied by the sine of the given angle. This is because the sine function represents the ratio of the opposite side to the hypotenuse in a right triangle, and by multiplying it with the length, we can calculate the actual length of the opposite side.

In simpler terms, multiplying a trigonometric function allows us to use the information we have about the angle and the length to find the missing side of a triangle. This is especially useful in real-world applications such as engineering, navigation, and physics, where accurate measurements and calculations are crucial.

Furthermore, trigonometric functions are also used to model and analyze various natural phenomena, such as sound waves and planetary orbits. By multiplying these functions, we can better understand and predict the behavior of these phenomena.

In conclusion, multiplying a trigonometric function is a fundamental aspect of trigonometry and has numerous practical and theoretical applications. It allows us to solve problems involving triangles and helps us understand the world around us. I hope this explanation helps you better understand the purpose and significance of this formula.