12$20Trigonometry - Trigonometry Geometry 12.1 The three...

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Geometry The three primary Trigonometric Ratios are Sine, Cosine, and Tangent. As we learned previously, triangles with the same angle measures have proportional sides. If you know one angle in a right triangle, you can use sin, cos, and tan to find the ratio of the lengths of its sides. Sine, Cosine, and Tangent Sin x o = Cos x o = Tan x o = 12.1 Trigonometry opposite hypotenuse adjacent hypotenuse opposite adjacent x o adjacent opposite hypotenuse Find sin x, cos x, and tan x in the right triangles below: 1. 2. Sin x o = Cos x o = Tan x o = x o 5cm 12cm 13cm 5cm 3cm 4cm x o If you know an angle, you can use a calculator to find the ratios: 1. sin 34 o = 2. cos 55 o = 3. tan 18 o = Sin x o = Cos x o = Tan x o = Use a calculator to find the missing lengths below: 1. 2. 5cm x y 27 o 58 o 22cm b a
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Geometry 12.1 Trigonometry You can use trigonometric inverses to find an angle based on a ratio: Sin, Cos, and Tan turn an angle into a ratio. Sin -1 , Cos -1 , and Tan -1 turn a ratio into an angle measure. Example: Find the measure of angle x in each triangle below: (make sure your calculator is set to degrees not radians) 1. 2. 5cm 12cm 13cm x o x o 109 in 60 in 91 in Practice: Find the missing information in each right triangle below: (round to the hundredth) 1. 2. 3. x o 15cm 11cm x 5cm 35 o x 9cm 15 o Practice: Find the apothem in each regular polygon below: 1. 2. 3. Find the sides. 8cm 10cm 6cm
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