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• ﻿Hello there everyone! For our today's lesson we will talk about 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 b and the adjacent side is a. Similarly, if the reference angle is A, then the opposite﻿ side is a and the adjacent side is b. Hence, the opposite side is the side opposite the reference angle, while the adjacent side is the side beside or next to the reference angle other than the longer side.
• A
• b﻿
• C﻿
• a﻿
• ﻿c
• ﻿B
• The following are the six ratios that can be named based on the relationships of the sides of a right triangle.
• 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). Using the sides of a right triangle, the definitions of trigonometric ratios of acute angle A areas follows: sin A = opposite side = a hypotenuse c cos A = adjacent side = b hypotenuse c tan A = opposite side = a adjacent side b
• 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 = c opposite a sec A = hypotenuse = c adjacent side b cot A = adjacent side = b opposite side a
• Note: Naming the opposite and adjacent sides of a right triangle depends on the reference angle.
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