# Trigonometry – One of the crucial branches of mathematics

One of the most important branches of mathematics is trigonometry. It has been a part of the math curriculum for a long time, and it has played an important role not only in solving mathematical problems but also in deriving derivations in physics and other subjects. It is a topic that demands not just a lot of practice but also a thorough comprehension in order to be proficient in trigonometry. In this article, we’ll look at what trigonometric ratios are and go over trigonometric identities also in detail.

**Trigonometric ratios:** Trigonometry itself consists of many numbers of concepts and is a vast field to comprehend. It will be easier for students to understand higher trigonometric concepts once they are clear with the basics. Thus, we will first discuss the most basic concept that is trigonometric ratios. Students are required to explore the relationship between the ratios of the various sides of a right-angled triangle and its angles in this field of mathematics. Trigonometry ratios are the ratios that we learn in trigonometry, and there are a total of six of them. Sine, cosine, tangent, cosecant, secant, and cotangent are the names for these functions.

These trigonometric ratios are extremely important, and every learner should understand what they mean. The ratio of the perpendicular of the triangle to the hypotenuse of the same triangle gives the sine of a right-angled triangle. The other ratio, cosine, represents the ratio of the base to the hypotenuse, while the tangent of a right-angled triangle is equal to the ratio of the perpendicular to the base. We have discussed three trigonometric ratios and these are the ones that need to be learnt first as the other three ratios that are left can be easily calculated by taking the help of the reciprocal trigonometric identities. Which we will discuss in trigonometric identities.

**Trigonometric identities:** Trigonometric identities can be considered as an equation that helps us to solve problems related to trigonometry, by providing us with the relation between different trigonometric functions. First, let us discuss the basic identity, that is reciprocal trigonometric identities. From the name itself, we can conclude that it is related to reciprocity. Suppose we are given cosecant then according to this identity, cosecant is the reciprocal of sine, similarly, secant is the reciprocal of cosec, and the cotangent of a right-angled triangle is the reciprocal of the tangent. In this way, one can easily relate all the six trigonometric ratios with one another. Now let us look at a few more trigonometric identities.

Apart from the above-mentioned identity, the other identity that finds huge importance in the field of trigonometry is Pythagorean Trigonometric identities. Like any other trigonometric identity, this one also gives us a unique relationship between different functions. The sum of the square of sine and square of cosine is always equal to unity, it can be represented as sin^{2}(theta) + cos^{2}(theta) = 1. This is one of the Pythagorean Trigonometric identities out of the three. The other two identities are 1 + tan^{2}(theta) = sec^{2}(theta) and 1+ cot^{2}(theta) = cosec^{2}(theta). These relations between different trigonometric functions are very crucial in solving problems. One needs to learn all the trigonometric identities to solve problems related to trigonometry easily.

In the preceding essay, we went over in-depth two of the most widely studied topics: trigonometric ratios and trig identities. Students should try to practice them as much as possible and gain a thorough understanding of them because they are fundamental concepts that will come in handy in further education. Cuemath is an online resource for students seeking assistance with math-related concepts. Students will get the opportunity to learn from the best teachers with Cuemath.