Knowledge is power as you will see. But where is the trig? This is the trig. That curve above is a special function. It's called the tangent function. 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".
I have never taken Trigonometry. I was wondering that if Trig is not as strongly required for Chemistry can I avoid taking it? You do need it for physics. At my school, you had to test into a math higher than the required pre-req or show proof of having taken the pre-req.
Since I had taken the pre-req at a different university several years earlier, I had to have an advisor override the system and register me for gen chem. Algebra is necessary for general chemistry and physics. Trigonometry is necessary for physics. As in, you really need to know it cold. Thanks guys for your reply! At the university I will be attending there are no pre-req for Gen Chemistry.
Is there anyway to study Trig on your own without taking a formal class? Also, my school offers Physics with Calculus and without. I was hoping to take Physics without Calculus and still apply to Med Schools requiring Calculus, assuming they would consider the Business Calculus I have taken as equivalent to regular Calculus. Challenger, if you had trigonometry in high school, you would be fine getting a workbook at Barnes and Noble and working through it.
Basically you need to know how to look at a triangle and create your own functions based thereon, to solve for the length of one side or the other.
This will be used to solve for vectors. In MCAT physics you are working with forces in two dimensions, therefore all forces can be plotted as the sum of horizontal and vertical vectors. If you know the combined force and the angle, with trig you can disaggregate into the horizontal and vertical components. If you know the horizontal and vertical components, you can determine the angle and the magnitude of the combined force.
Etc etc ad nauseum.
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