Trigonometric Formula 1
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Trigonometric functions are defined based on ratios of sides of a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Inverse trig functions like cotangent, secant, and cosecant are defined based on the reciprocals of the primary trig functions.
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This document discusses how to use trigonometric ratios (SOH CAH TOA) to solve for unknown sides of a right triangle. It explains that SOH relates sine to the opposite and hypotenuse sides, CAH relates cosine to the adjacent and hypotenuse sides, and TOA relates tangent to the opposite and adjacent sides. The document provides step-by-step instructions: 1) name the sides of the triangle based on the given angle, 2) use SOH, CAH or TOA to identify the appropriate ratio, 3) write the ratio as a fraction and plug in known values, 4) use a calculator to solve for the last side.
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1.1.2 Soh Cha Toa
This document defines the trigonometric functions of sine, cosine, and tangent by relating the ratios of opposite, adjacent, and hypotenuse sides of a right triangle to the angle θ. It then provides examples of using these definitions to calculate the sine, cosine, and tangent of an angle where the lengths of the sides of a right triangle are given. The document directs the reader to additional trigonometry resources for more information.
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The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides the Law of Sines formula that relates the ratios of sides to opposite angles. It gives two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It also provides the formula to find the area of a triangle using two sides and the included angle. Several example problems are worked through applying the Law of Sines to find missing side lengths and triangle areas.
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This document discusses how to use trigonometric ratios (SOH CAH TOA) to solve for unknown sides of a right triangle. It explains that SOH relates sine to the opposite and hypotenuse sides, CAH relates cosine to the adjacent and hypotenuse sides, and TOA relates tangent to the opposite and adjacent sides. The document provides step-by-step instructions: 1) name the sides of the triangle based on the given angle, 2) use SOH, CAH or TOA to identify the appropriate ratio, 3) write the ratio as a fraction and plug in known values, 4) use a calculator to solve for the last side.
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This document defines the trigonometric functions of sine, cosine, and tangent by relating the ratios of opposite, adjacent, and hypotenuse sides of a right triangle to the angle θ. It then provides examples of using these definitions to calculate the sine, cosine, and tangent of an angle where the lengths of the sides of a right triangle are given. The document directs the reader to additional trigonometry resources for more information.
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The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides the Law of Sines formula that relates the ratios of sides to opposite angles. It gives two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It also provides the formula to find the area of a triangle using two sides and the included angle. Several example problems are worked through applying the Law of Sines to find missing side lengths and triangle areas.
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