Basic trigonometry formula

Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin(x), cos(x), and tan(x), where x is an angle in radians or degrees. Created by Sal Khan. Well, in beginning trigonometry, it's convenient to evaluate sin/cos/tan by using soh-cah-toa, but later, as you get into the unit circle and you start taking taking stuff like sin(135) and tan(-45) you don't use the adjacent-opposite-hypotenuse much anymore. If you can think of it intuitively, though, sin(90) means that the opposite side is infinitely long, and the hypotenuse is also infinitely long, so sin(90)=1. cos(90) means adjacent over the hypotenuse, which is infinitely long given that the angle is 90 degrees, so any number over infinity is 0, so cos(90)=0. tan(90)=sin(90)/cos(90)=1/0, so tan(90) doesn't exist. A small question. We name the ratios as "Sine", "Cosine", "Tangent", "Cotagent", "Secant" and "Cosecant". The last four can be drawn of circle. Is "Sine" also a part of circle. I mean can it be drawn on circle like tangent and secant. I know its a useless question, but I was just wondering. Thanks for your time. I think that's a great question! This is a pretty cool story (to me at least). The word that the Arabs used for sine was the same as their word for "chord", but whe...

\( \newcommand\) • • • • • • • • • • • • • • • • • • • • • • • Learning Objectives • Verify the fundamental trigonometric identities. • Simplify trigonometric expressions using algebra and the identities. In espionage movies, we see international spies with multiple passports, each claiming a different identity. However, we know that each of those passports represents the same person. The trigonometric identities act in a similar manner to multiple passports—there are many ways to represent the same trigonometric expression. Just as a spy will choose an Italian passport when traveling to Italy, we choose the identity that applies to the given scenario when solving a trigonometric equation. Figure \(\PageIndex\): International passports and travel documents In this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions. Verifying the Fundamental Trigonometric Identities Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations. In fact, we use algebraic techniques constantly to simplify trigonometric expressions. Basic properties and formulas of algebra, such as the difference of squares formula and the perfect squares formula, will simplify the wor...

• • • • • • • • • • • In simple language, trigonometry can be defined as that branch of algebra, which is concerned with the triangle. In this branch, we study the relationship between angles and the side length of a given triangle. With this detailed study of triangles, several types of equations are formed, which are consequently solved to simplify the relationship between the side and angle lengths of such triangles. Formula of Trigonometry Well, whether it is algebra or geometry both of these mathematics branches are based on scientific calculations of equations and we have to learn the different formulas to have easy calculations. As we know that in Trigonometry we measure the different sides of a triangle, by which several equations are formed. Further, the formulas of Trigonometry are drafted following the various ratios used in the domain, such as sine, tangent, cosine, etc. So, there are the numbers of the formulas which are generally used in Trigonometry to measure the sides of the triangle. Here below we are mentioning the list of different types of formulas for Trigonometry. • Trigonometry Basic Formula 2. Sin Cos Tan at 0, 30, 45, 60 Degree 3. Pythagorean Identities 4. Sign of Sin, Cos, Tan in Different Quadrants A dd– Sugar–To –Coffee 5. Radians 1 Degree = 60 Minutes Ex: 1 °= 60′ 1 Minute = 60 Seconds Ex: 1′ = 60” 6. Negative Angles [Even-Odd Identies] Sin (-x) = – Sin x Cos (-x) = Cos x Tan (-x) = – Tan x Cot (-x) = – Cot x Sec (-x) = Sec x Cosec (-x) = – Co...

\( \newcommand\) • • • • • • • • • • • • • • • • • • • • • • • Learning Objectives • Verify the fundamental trigonometric identities. • Simplify trigonometric expressions using algebra and the identities. In espionage movies, we see international spies with multiple passports, each claiming a different identity. However, we know that each of those passports represents the same person. The trigonometric identities act in a similar manner to multiple passports—there are many ways to represent the same trigonometric expression. Just as a spy will choose an Italian passport when traveling to Italy, we choose the identity that applies to the given scenario when solving a trigonometric equation. Figure \(\PageIndex\): International passports and travel documents In this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions. Verifying the Fundamental Trigonometric Identities Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations. In fact, we use algebraic techniques constantly to simplify trigonometric expressions. Basic properties and formulas of algebra, such as the difference of squares formula and the perfect squares formula, will simplify the wor...

• • • • • • • • • • • In simple language, trigonometry can be defined as that branch of algebra, which is concerned with the triangle. In this branch, we study the relationship between angles and the side length of a given triangle. With this detailed study of triangles, several types of equations are formed, which are consequently solved to simplify the relationship between the side and angle lengths of such triangles. Formula of Trigonometry Well, whether it is algebra or geometry both of these mathematics branches are based on scientific calculations of equations and we have to learn the different formulas to have easy calculations. As we know that in Trigonometry we measure the different sides of a triangle, by which several equations are formed. Further, the formulas of Trigonometry are drafted following the various ratios used in the domain, such as sine, tangent, cosine, etc. So, there are the numbers of the formulas which are generally used in Trigonometry to measure the sides of the triangle. Here below we are mentioning the list of different types of formulas for Trigonometry. • Trigonometry Basic Formula 2. Sin Cos Tan at 0, 30, 45, 60 Degree 3. Pythagorean Identities 4. Sign of Sin, Cos, Tan in Different Quadrants A dd– Sugar–To –Coffee 5. Radians 1 Degree = 60 Minutes Ex: 1 °= 60′ 1 Minute = 60 Seconds Ex: 1′ = 60” 6. Negative Angles [Even-Odd Identies] Sin (-x) = – Sin x Cos (-x) = Cos x Tan (-x) = – Tan x Cot (-x) = – Cot x Sec (-x) = Sec x Cosec (-x) = – Co...

Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin(x), cos(x), and tan(x), where x is an angle in radians or degrees. Created by Sal Khan. Well, in beginning trigonometry, it's convenient to evaluate sin/cos/tan by using soh-cah-toa, but later, as you get into the unit circle and you start taking taking stuff like sin(135) and tan(-45) you don't use the adjacent-opposite-hypotenuse much anymore. If you can think of it intuitively, though, sin(90) means that the opposite side is infinitely long, and the hypotenuse is also infinitely long, so sin(90)=1. cos(90) means adjacent over the hypotenuse, which is infinitely long given that the angle is 90 degrees, so any number over infinity is 0, so cos(90)=0. tan(90)=sin(90)/cos(90)=1/0, so tan(90) doesn't exist. A small question. We name the ratios as "Sine", "Cosine", "Tangent", "Cotagent", "Secant" and "Cosecant". The last four can be drawn of circle. Is "Sine" also a part of circle. I mean can it be drawn on circle like tangent and secant. I know its a useless question, but I was just wondering. Thanks for your time. I think that's a great question! This is a pretty cool story (to me at least). The word that the Arabs used for sine was the same as their word for "chord", but whe...