How does trigonometry relate to physics

If you put an angle into this function, it gives you the ratio of y to x. You could write this tangent function as:. But remember it's just a function. Let's look at another function. But if I use the triangle above, I only get angles from 5 to 80 degrees. I want MORE angles. What if instead of keeping the x side of the triangle constant, I keep the hypotenuse constant? In that case you can imagine a line of fixed length sweeping around a set point.

As this set line sweeps around, it would create a circle. AH HA! You knew trig was really about circles. Alas, not really. It just happens that it's easy to show trig functions with a circle, but trig functions are really about right triangles. Don't be fooled.

Let's draw a bunch of triangles. You can do this too. I'm just going to take an old CD you know Then I'm going to approximate the location of the center and draw a bunch of triangles.

The numbers next to the lines for the different triangles are just my measurements of the y side length in centimeters. I drew a triangle for angles at 10 degree increments so I should be easy to figure out the angle for each triangle. I recommend drawing your own set of triangles. You can't really understand something just by looking at it; you have to do it yourself it's not hard. Two things to notice before getting to the graph. First, what I call "y" could also be called the "opposite" side of the triangle.

Second, if the y side of the triangle is below the x-axis I'm going to give it a negative length. That will be useful later. Here is my plot of opposite over hypotenuse vs. Remember, these are actual measurements from actual triangles so it's not perfect. Check that out. Are you excited? I am surprisingly excited that this worked out fairly nicely. You should be excited too, but if you aren't that's OK I guess. But your eyes do not deceive you.

That is indeed the sine function. This function is very similar to the tangent function except that it is the ratio of the opposite side of the triangle opposite from the angle and the hypotenuse. You could also calculate the ratio of the adjacent side divided by the hypotenuse—we call this the cosine function.

OK, now for some important notes on these functions. One other very important point. If you are using angles in degrees, make sure your calculator or your lookup table is in degrees. If you are using radians, then your calculator needs to be in radians mode. You would not believe how often I see students make this mistake. But what is the difference between radians and degrees? Let's go over that. First, I guess we should talk about degrees. Why are there degrees for a full circle?

Why not degrees? Wouldn't that make more sense? Actually, no. You can divide it by 2, 3, 4, 5, 6, 8, 9, This means that by breaking a circle into "parts," you can also break it into many other parts.

This is great if you are dealing with fractions instead of decimals. So, that's why we have the unit of degrees. What about radians? How about this? Consider just part of a circle. Something like this. It would be fun to actually draw something like this. You could then measure the value of r the radius the angle and the arc-length s.

You could also calculate the arc-length. Since this is part of a circle, the arc-length would be with the angle in measured in degrees :. Essentially this takes the angle as a fraction of the total circle. That means the arc-length will be a fraction of the circumference of the circle. But wait! What if we just use an angle that doesn't have to do this silly fraction?

What if we write the arc-length as:. Boom—that's your angle measurement in radians. It allows us to make a fraction-less connection between the angle and the arc-length. In many ways it's better than an angle measured in degrees since it's more "natural". But now for the last question: why do we even need trig? Or perhaps you might ask, who cares about right triangles?

You care. At least you should care. The main reason but not the only to use trig is for vectors. Trigonometry used in navigation: Trigonometry is used to set directions such as the north south east west, it tells you what direction to take with the compass to get on a straight direction. Other uses of trigonometry: It is used in oceanography in calculating the height of tides in oceans.

The sine and cosine functions are fundamental to the theory of periodic functions, those that describe the sound and light waves. Calculus is made up of Trigonometry and Algebra. Trigonometry can be used to roof a house, to make the roof inclined in the case of single individual bungalows and the height of the roof in buildings etc. It is used naval and aviation industries. It is used in cartography creation of maps.

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