Simply About the Complex Sine And Cosine

Just about the complex sinus and cosine!

To many students, the concepts of sine, cosine, tangent, cotangent seem complex, but in fact they are simple. You just need to visualize some concepts and clearly understand them for yourself.

For this I propose to stock up on improvised items, such as pens, pencils, stapler, marker, eraser, etc., and be sure to use a measuring ruler and make a demonstration. Everything will be easier than you think!

We will collect from our objects a right-angled triangle with sides A, B, C and angle Y.

The usual triangle you will say is not as remarkable as in any textbook. But still have the patience and we will continue. Take a ruler and measure the side B, you have it is an object, let's say a pencil. Measure the length of the pencil and round off the resulting measurement result to centimeters. Our side B is assumed to be equal to three centimeters. Let's measure side A. Five centimeters. Now divide the length of side A by the length of side B. This will be the ratio of A to B = A / B = 5/3, you can divide D by A and get 3/5, C on B, and so on.

Now let's increase the triangle. Let's extend sides A, B and C. Do this with the help of your office supplies.

Now the sides of the triangle A, B, C will turn into A, T, A. Let us measure the sides of D and F, their ratio is 10/6. And so Д / Г = 10/6 = 5/3. The attitude of other relevant parties is also not changed. You can measure the length, but you can believe it. This is everyone's business! You can arbitrarily change the lengths of the sides in a right-angled triangle, increase, decrease, without changing the angle Y - the ratio of the corresponding sides will not change.

And if you change the angle Y, increase or decrease it, then all the relations of the lengths of the sides change. See for yourself.

As promised earlier, everything is simple. Let's draw conclusions. The relations of the sides in a right-angled triangle do not depend on the lengths of the sides (at the same angle), but depend sharply on this angle. And all these relations of the parties have, of course, names:

SIN Y = A / C. The sine of the angle Y is the ratio of the opposing leg (far from the corner) to the hypotenuse.

COS Y = B / S. Cosine of angle Y This is the ratio of the adjacent leg (proximal) to the hypotenuse.

Sine and cosine are trigonometric functions, and in a simple sense, some numbers, for each corner of their own. As it turned out, everything is very simple.

Sine and cosine are direct trigonometric functions. Derivatives will be trigonometric functions such as tangent (tg x) and cotangent (ctg x).

Other trigonometric functions are secant (sec x) and cosecant (cosec x), but most likely they will not occur to you so often. In addition to these six, there are also some rarely used trigonometric functions (version, etc.), as well as trigonometric functions (arcsine, arc cosine, etc.).

I hope you understand everything and can apply!