TRIGONOMETRIC RATIOS OF ACUTE ANGLES

“Trigonometric” ratios of acute angles have been defined as the ratio of any side of a triangle. This angle has acute values that are important to make effective solutions in trigonometric mathematics. The explanation of trigonometric ratios of acute angle has been discussed in this study. Besides, the explanation of the “trigonometry table” with describing trigonometric tools has been analyzed in the second part of the study. Moreover, some essential formulas have been defined and analyzed to show their importance. Some questions and answers related to table and formulas have been described below. Moreover, the relation between table  and formulas  has been  defined  in this study.  

Explanation about trigonometric ratios of acute angles

Trigonometric ratios of acute angles have been constructed based on the ratio of length, base, and hypotenuse of a right-angled triangle. Besides, these ratios have individual names that are based on different positions of length, base, and hypotenuse. Moreover, these trigonometric equalities have separate values based on their angle position. Some major trigonometric equality has been described below. Assume ϴ is the angle between length and base. 

“sinϴ” = length/hypothesis 

“coosϴ” = base / hypothesis

“tanϴ” = length/base  

“cosecϴ” = hypothesis /length

“secϴ” = hypothesis / base

“cotϴ” = base/ length

Explanation of the trigonometry table 

As per the basis of the Pythagoras trigonometric rules, some majors have been created that are used to conduct mathematics equations in the sum.  

The major trigonometric equalities are “sine”, “cosine”, “tangent”, “cosecant”, “secant”, and “cotangent”.” that has different values by using different angles. There are six major angels presented in this study that includes “0o”, “30o”, “60o”, “45o”, and “90o”.

By putting these angle values in the trigonometric equalities, different rational values have been found. Assume “Θ” is the angle that has been situated in the right-angled triangle. Based on an assumption six trigonometric equalities have been constructed below.

“Sin Θ”,   “cosϴ”, “tanϴ”, “cosecϴ” , “secϴ” and  “cotΘ”.

By putting the value of “Θ” in “0o,” “30o,” “60o,” “45o,” and “90o” then the value of the trigonometric equalities are 

“Sin 0o” = zero, “Sin30o”= ½, “Sin 45o” = 1/√2, “Sin 60o” = √3/2 and “Sin 90o” = one. As per the value has been represented the ratio of  the length and hypotenuse of a right  angle  triangle  whose variables  angle  values “0o”, “30o”, “60o”, “45o”, and “90o”.

Similarities

In cosine  

“Cos 0o” = 1, “Cos 30o”= √3/2, “Cos45o” = 1/√2, “Cos 60o” = 1/2 and “Cos 90o” = 0

“Tan0o” = 0, “Tan 30o”= 1/√3,”Tan45o” = 1,”Tan 60o” = √3 and “Tan 90o” = infinity 

“Cosec 0o” = infinity, “Cosec 30”= 2,”Cosec 45o” = √2,”Cosec 60” = 2/√3 and “Cosec 90” =1

“Sec 0o” = 1,”Sec30o”= 2/√3, “Sec45o” = √2, “Sec 60o” =  2 and “Sec 90o” =  infinity  

“Cot 0o” = infinity,”Cot30o”= √3, “Cot45o” = 1, “Cot 60o” = 1/√3 and “Cot 90o” =  0

Explanation of the trigonometric formula  

Trigonometry formulas are a major part of the math that has been used to solve the sum. Besides, the trigonometry formulation has been represented as the equation. These equations have been constructed with the help of trigonometry equities. Through the one formula, different kinds of other trigonometry formulas can be constructed. Some major formulas have been defined that are essential for conducting trigonometric sums in the mathematics parts. In addition, the formulas are the ethical values that have been constructed by using geometric processing. Moreover, there are different rules and formulas that have been involved in trigonometric mathematics that are important for conducting trigonometric solutions in mathematics. 

The formulas have been defined below as part of the study.

“(sin2Θ + cos2Θ)” = 1

“(sec2Θ -tan2Θ)” = 1

“(Cosec2Θ – cot2Θ)” = 1

This is the equation form formulas that have been used to get the value of “Sin Θ”,   “cosΘ”, “tanΘ”, “cosecΘ”, “secΘ” and  “cotΘ”.

Periodic types of trigonometric formulas

“Sin (π/2 – Θ)” = “cos Θ”

Degree types of trigonometric formulas

“Sin (90o – Θ)” = “cos Θ” 

Half angle types of trigonometric formulas

“Sin (Θ/2)” = “±√ [(1 – cos  Θ)/2]”

Double angle identities of trigonometric formulas

“Sin (2Θ)” = “2sin (Θ) • cos (Θ)” = “[2tan Θ / (1 + tan2 Θ)]”

Relation between trigonometry table and trigonometric formula

There is a huge connection between trigonometry tables and trigonometric formulas in math. Based on the values of trigonometric angle it has to be put in the trigonometric equation to find out numerical values for the sum. 

Conclusion  

Throughout the study, it has been conducted all about trigonometric ratios of acute angles. This triangle formula has been constructed by using the trigonometric identities with the help of the Pythagoras rules that have mathematical formulas based on the high, base, and hypotenuse. A brief explanation of the trigonometric table has been provided in this study above. Moreover, some essential formulas and the relation between trigonometry table and trigonometric formula have been described above.