- Hello there everyone! For our today's lesson we will talk about Six Trigonometric ratios.
- The Trigonometric Ratios are the relationships of the two sides of a right triangle. The sides are labelled as the opposite side, adjacent side, and the hypotenuse, which is the longest side.The opposite side and the adjacent side are determined through the reference angle, which is any of the acute angles of a right triangle
- Based on the figure above, if the reference angle is B, then the opposite side is 3 and the adjacent side is 4. Similarly, if the reference angle is A, then the opposite side is 4 and the adjacent side is 3.
- A
- 3
- C
- 4
- 5
- B
- The following are the six ratios that can be named based on the relationships of the sides of a right triangle.sin= opposite csc= hypotenuse hypotenuse oppositecos= adjacent sec= hypotenuse hypotenuse adjacenttan= opposite cot=adjacent adjacent hypotenuse
- The relationships of the two sides of a right triangle are described by the trigonometric ratios such as sine (abbreviated as sin), cosine (abbreviated as cos), tangent (abbreviated as tan), cosecant (abbreviated as csc), secant (abbreviated as sec), and cotangent (abbreviated as cot). The three basic trigonometric ratios are SOH-CAH-TOA. sin A = opposite side = 4 hypotenuse 5cos A = adjacent side = 3 hypotenuse 5tan A = opposite side = 3 adjacent side 4
- Just remember the mnemonic SOHCAHTOA when solving trigonometric ratios. SOH stands for sine equals opposite over hypotenuse; CAH means cosine equals adjacent over hypotenuse; and TOA stands for tangent equals opposite over adjacent.
- csc A = hypotenuse = 5 opposite 4 sec A = hypotenuse = 5 adjacent side 3cot A = adjacent side = 3 opposite side 4
- Note: Naming the opposite and adjacent sides of a right triangle depends on the reference angle.
- The secondary trigonometric ratios are reciprocal of SOH-CAH-TOA

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