The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles. Show
The trigonometry ratios for a specific angle ‘θ’ is given below:
Note: Opposite side is the perpendicular side and the adjacent side is the base of the right-triangle. Also, check out trigonometric functions to learn about each of these ratios or functions in detail.Trigonometric Identities Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle. The three sides of the right triangle are:
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How to Find Trigonometric Ratios?Consider a right-angled triangle, right-angled at B. With respect to ∠C, the ratios of trigonometry are given as:
The above ratios are abbreviated as sin, cos, tan, cosec, sec and tan respectively in the order they are described. So, for Δ ABC, the ratios are defined as: sin C = (Side opposite to ∠C)/(Hypotenuse) = AB/AC cos C = (Side adjacent to ∠C)/(Hypotenuse) = BC/AC tan C = (Side opposite to ∠C)/(Side adjacent to ∠C) = AB/BC = sin ∠C/cos ∠C cosec C= 1/sin C = (Hypotenuse)/ (Side Opposite to ∠C) = AC/AB sec C = 1/cos C = (Hypotenuse)/ (Side Opposite to ∠C) = AC/BC cot C = 1/tan C = (Side adjacent to ∠C)/(Side opposite to ∠C)= BC/AB In right Δ ABC, if ∠A and ∠C are assumed as 30° and 60°, then there can be infinite right triangles with those specifications but all the ratios written above for ∠C in all of those triangles will be same. So, all the ratios for any of the acute angles (either ∠A or ∠C) will be the same for every right triangle. This means that the ratios are independent of lengths of sides of the triangle. Trigonometric Ratios TableThe trigonometric ratios for some specific angles such as 0 °, 30 °, 45 °, 60 ° and 90° are given below, which are commonly used in mathematical calculations.
From this table, we can find the value for the trigonometric ratios for these angles. Examples are:
Trigonometry ApplicationsTrigonometry is one of the most important branches of mathematics. Some of the applications of trigonometry are:
It is evident from the above examples that trigonometry has its involvement in a major part of our day-to-day life and much more. In most of the applications listed above, something was being measured and that is what trigonometry is all about. Solved ProblemsQ.1: If in a right-angled triangle ABC, right-angled at B, hypotenuse AC = 5cm, base BC = 3cm and perpendicular AB = 4cm and if ∠ACB = θ, then find tan θ, sin θ and cos θ. Sol: Given, In ∆ABC, Hypotenuse, AC = 5cm Base, BC = 3cm Perpendicular, AB = 4cm Then, tan θ = Perpendicular/Base = 4/3 Sin θ = Perpendicular/Hypotenuse = AB/AC = ⅘ Cos θ = Base/Hypotenuse = BC/AC = ⅗ Q.2: Find the value of tan θ if sin θ = 12/5 and cos θ = ⅗. Sol: Given, sin θ = 12/5 and cos θ = ⅗ As we know, Tan θ = Sin θ/Cos θ Tan θ = (12/5)/(⅗) Tan θ = 12/3 Tan θ = 4 Practice Questions
Video LessonTrigonometric Ratios of Compound AnglesDownload BYJU’S App and learn thousands of concepts here through interesting and personalised videos. Frequently Asked Questions – FAQsThe three primary trigonometric ratios are tangent (tan), sine (sin) and cosine (cos). What are the six trigonometric ratios?The six 6 trigonometric ratios are sine, cosine, tangent, cotangent, cosecant, and secant. What is SOH CAH TOA?SOH CAH TOA is the mnemonic to remember the formula for
trigonometry ratios, such that: What is the formula for Cotangent, Secant and Cosecant?Cotangent is the ratio of Adjacent side and Opposite side, (Base/Perpendicular) What is the relationship between sin, cos and tan?Tangent functions is equal to the ratio of sine and cosine function. What are the six trigonometric functions?There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
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