CONCEPT OF EQUATIONS, ANGLES, AND IDENTITIES

Trigonometry plays an important role in scientific as well as geographical study. Even though trigonometry is not required to make day-to-day calculations, there are some mathematical calculations that can not be performed without the help of trigonometric formulas and trigonometric values. The measurement of angular distance and the distance between two long distances, the height of mountains, etc are measured with the help of trigonometric functions and formulas. Therefore, it is important to know the basics of trigonometry, how the formulas are derived, and how the trigonometric values are identified. In addition to this, the trigonometric equations need to be analyzed. The Pythagorean Theorem needs to be considered along with its components such as the base, perpendicular, and hypotenuse of a triangle with an angle measuring 90 degrees to derive trigonometric formulas.

CONCEPT OF EQUATIONS AND ANGLES

Trigonometry is the study of the relationship between the angles as well as the sides of a triangle. Moreover, it can be said that trigonometry is a branch of study that specifically deals with angles. There are many types of angles existing in the field of geometry such as acute, obtuse, straight, right, reflex, and full rotation angles. The acute angle is an angle that is always less than 90 degrees. On the other hand, obtuse angle measures more than 90 degrees, whereas in the case of “reflex angle” the measurement is more than 180 degrees but less than 360 degrees.. In the case of a full rotation, the value of the angle is 360 degrees. There are certain trigonometric identities from which other identities can also be derived.

The basic trigonometric equations are “Sin2 a + cos2a” = “1”, “1+tan2 a” = “sec2 a”, “cosec2a” = “1 + cot2 a” which are derived from the Pythagorean model, and can be termed as trigonometric equations. There are some trigonometric formulas that play a significant role in mathematical calculations such as, “sin (x-y)  equals to sinxcosy – cosxsiny”, “cos(x-y)”  equals to  “cosx cosy +sinxsiny”, , and “cos (x+y) is significant to cosxcosy – sinx siny, “sin(x+y)” amounts to “sinx cosy + cosx siny””. Apart from these some intricate trigonometric formulas need to be taken into consideration such as the trigonometric functions of tan, cot, sec, cot, and cosec to put them into equations. The trigonometric formulas give specific fic identities to the trigonometric identities. Therefore, ther trigonometric equation can be derived using these formulas and functions on the basis of trigonometric ratios. On the other hand, the study also initiates a critical understanding of the formulas.

EXPLANATION OF TRIGONOMETRIC FORMULAS

Trigonometric identities are derived from a triangle that contains an angle measuring 90 degrees. Trigonometric identities are based on trigonometric ratios that are derived from a triangle that has a right angle. The major components of a triangle with a right angle are the perpendicular, base, and hypotenuse. The trigonometric ratios are determined with the help of the measurements of the perpendicular, hypotenuse, and the base of a triangle that has a right angle. The basic trigonometric identities are “sin, cosine, sec, cosec, tan, cot, and cotangent”. In the case of studying trigonometric functions, it is necessary to understand the sides of a triangle with an angle measuring 90 degrees. In the case of “Sin,” the relationship between the components of the triangle with a right angle is opposite side/ Hypotenuse, whereas in the case of cos it is “Adjacent side by Hypotenuse”. On the other hand, tan refers to the opposite side/ adjacent side. In addition to this, “secant function” refers to the relationship between the hypotenuse and adjacent side, i.e. hypotenuse/ adjacent side. “Cotangent” function or “Cot” is just the inverse of “tan”, and that becomes the “adjacent side by the opposite side”. Lastly, the “cosec function” is derived from the ratio of Hypotenuse and opposite side. Interestingly, there are odd trigonometric functions as well as even trigonometric functions. There are some trigonometric angles on the basis of which the trigonometric values are derived. These angles are “90”, “30”, “0”, “60”, “45” degrees”

Trigonometric values are essential to solve a trigonometric problem, and there is a process of deriving these values.  For cos, sin, cosec, sec, tan, and cot the values are very different under the angles such as 0, 45, 30, 90, and 60 degrees. There are individual values attached to every trigonometric identity. The trigonometric values are constant and universal, for example, the value of tan45o is 1, whereas cot45 is just the inverse of tan which is equal to 1. For Cot the values are “√3”, “1/√3” infinity,“1”, and for “0”, “30”, “45”, “0”, and “90” respectively. Similarly, there are all unique values for cos, sec, and sin.

Conclusion

There are many trigonometric equations that are derived from the trigonometric identities and the radians that help to an extreme the measurement of the angles. In addition to this, the above analysis clearly states that the trigonometric formulas are interlinked with each other, and there are certain factors with respect to trigonometric values that make every trigonometric identity unique and relevant. The trigonometric ratios play a significant role in the formation of the trigonometric identities that form an integral part of trigonometry as a field of mathematics. The trigonometric values are put in the equation to get the solution to the trigonometric problem.