In any right angled triangle. We will discuss two methods to learn sin cos and tang formulas easily. Students need to remember two words and they can solve all the problems about sine cosine and tangent.
So now we disucss how it works to remember the formula. The first angle goes, "Hey Thelma or is it Theta? Of course, that means that if you don't know the difference between a sine and a cosine, you're currently left out in the metaphorical cold.
Clearly we can't let that happen—and we won't! Because today we're going to learn all about sines, cosines, and tangents. Recap: trigonometry and triangles When we talked about the world of trigonometry , we learned that the part of math called trigonometry deals with triangles.
And, in particular, it's the part of math that deals with figuring out the relationship between the three sides and the three angles that make up every triangle. 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.
The word "hypotenuse" comes from two Greek words meaning "to stretch", since this is the longest side. We label the hypotenuse with the symbol h. There is a side opposite the angle c which we label o for "opposite". The remaining side we label a for "adjacent".
The angle c is formed by the intersection of the hypotenuse h and the adjacent side a. We are interested in the relations between the sides and the angles of the right triangle. Let us start with some definitions. We will call the ratio of the opposite side of a right triangle to the hypotenuse the sine and give it the symbol sin. The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.
We claim that the value of each ratio depends only on the value of the angle c formed by the adjacent and the hypotenuse. To demonstrate this fact, let's study the three figures in the middle of the page. Sine, Cosine and Tangent are the names of three of the comparisons between the lengths of the sides of a right-angled triangle.
Trigonometry deals with the sides and angles in triangles and the relationship between them. In a right-angled triangle, the sides are named according to the each of the acute angles,. The side next to an angle one of its arms is called the adjacent side while the side on the other side from the angle is called the opposite side. In trigonometry the lengths of the 3 sides are compared in the form of ratios.
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