Analysis Of T-Ratio At Some Standard Angles

Trigonometry is an important branch of mathematics that deals with several functions and ratios, which function as the basis of numerous problems and concepts. Trigonometric ratios are the ratio of two branches of a right-angled triangle with different branches for the ratio for particular trigonometric ratios. This article will provide you with a detailed guide on trigonometric ratios with a trigonometric ratios table(standard angles) along with some derivation of trigonometric ratios of standard angles and trigonometric ratios formulas. Now that you have become familiar with trigonometric functions and ratios, let’s start with a brief introduction to trigonometric functions and ratios.

Trigonometric functions and ratios

Trigonometric functions include six particular functions that derive the ratios we use for further calculations and other needs. There are six trigonometric functions:

• Cosecant
• Secant
• Cotangent
• Sine
• Cosine
• Tangent 

These functions are transformed into trigonometric ratios with their formulation process. Each of these six trigonometric functions is calculated by taking the ratios of any two sides of a right-angled triangle depending on the function we are calculating. The formulas for calculating trigonometric ratios are given below:

Here is a trigonometric ratios table(standard angles) to understand the trigonometric ratios better.

Standard angles

are defined as some particular angles whose values of trigonometric ratios are particular for uses. These angles are

• 0°
• 30°
• 45°
• 60°
• 90°.

Now that you have become familiar with the concept of trigonometric functions, trigonometric ratios, and standard angles. Let us look at the trigonometric ratios table(standard angles) given below for a better understanding of the concept.

This table elaborates the formulas required to transform the trigonometric functions into trigonometric ratios. Now let’s look at the trigonometric ratios table(standard angles).

The trigonometric ratios table(standard angles) given above gives a clear understanding of the concept of trigonometric functions and their ratio values for some standard angles.

Derivation of trigonometric ratios for standard angles

Let us suppose we have a right-angled triangle with base AB, height AC, and hypotenuse BC. Now, if this triangle is right-angled it means that A is the right angle and the other two angles are acute angles. Let us assume that these two angles are equal, it means angles B and C are 45°. 

Conclusion

Trigonometric ratios are the basics of mathematics, and the results of some standard angles are used for further calculations in complex problems of mathematics. Primary trigonometric ratios include sine, cosine, and tangent, which are further used to derive the formulas for trigonometric ratios like cosec, sec, and cot. These trigonometric ratios are essential to solving complex mathematical problems, and they are used as a base to derive other values by splitting them into smaller parts. This article has provided a trigonometric ratios table(standard angles) and the formulas and derivation of trigonometric ratios for standard angles.