Of particular interest to us is the special type of triangles known as right triangles. Every right triangle has one degree angle like the corner of a square or rectangle , and two angles that each range between anything larger than 0 degrees and smaller than 90 degrees with, as we'll talk about in the future, the sum of all 3 angles being degrees. For our discussion of sine, cosine, and tangent which, don't worry, are not as complicated as they sound , it's important that we have a way of labeling the sides of right triangles.
As we learned last time , the longest side of a triangle is known as its "hypotenuse. And the side adjacent to the angle we're looking at the one that isn't the hypotenuse is known as the "adjacent" side.
Sine, cosine, and tangent With all of these preliminaries now happily splashing around inside our growing pool of mathematical knowledge, we're finally ready to tackle the meaning of sine, cosine, and tangent. Here's the key idea: The ratios of the sides of a right triangle are completely determined by its angles. The ratios of the sides of a right triangle are completely determined by its angles. In other words, the value you get when you divide the lengths of any two sides of a right triangle—let's say the length of the side opposite one of its angles divided by its hypotenuse—is entirely set in stone as soon as the angles are set in stone.
Well, if the angles are fixed, making the triangle bigger or smaller has no impact on the relative lengths of its sides. But changing the triangle's angles, even a tiny bit, does!
If you need some convincing, try drawing a few triangles of your own and you'll see that it is indeed true. Now, the fact that there are three sides of a triangle means that there are also three possible ratios of the lengths of a triangle's sides. And, as you might have already guessed, these three ratios are none other than the famous sine, cosine, and tangent trigonometric functions. The sine of one of the angles of a right triangle often abbreviated "sin" is the ratio of the length of the side of the triangle opposite the angle to the length of the triangle's hypotenuse.
The cosine often abbreviated "cos" is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. And the tangent often abbreviated "tan" is the ratio of the length of the side opposite the angle to the length of the side adjacent. Since this is kind of a mouthful and a little hard to remember, kind folks over the centuries have come up with a handy mnemonic to help you and countless generations of kids in school out.
How will you use sine, cosine, and tangent outside the classroom, and why is it relevant? There are a few career paths that lead to constant use of these equations. For example, lets say you're a sound engineer working on the production of a hit artist's new album. You know that sound travels in waves, and engineers can manipulate these waves measured by and applying trigonometry to create different computer-generated sounds.
What if you're an architect who needs to know the height of an existing building in a neighborhood you're assigned? You can use the distance you are from the building and the angle of elevation to detemine the height.
It represents a mathematical curve depicting a repetitive oscillation motion similar to a cosine function. Difference between Sine and Cosine Wave. Key Difference: Sine and cosine waves are signal waveforms which are identical to each other.
The main difference between the two is that cosine wave leads the sine wave by an amount of 90 degrees. Image Courtesy: reddit. How do you find the measure of the smallest in an acute triangle whose side lengths are 4m, 7m, and 8m? Bong walks m due North and then m in a direction N 37 deg. How far is Bong from his See all questions in The Law of Cosines.
Impact of this question views around the world. You can reuse this answer Creative Commons License.
0コメント