 # Unit J.1-J.2 Trigonometric Ratios

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Unit J.1-J.2 Trigonometric Ratios
Tuesday, Feb 28 Trigonometry Ratios Find the tangent, sine and cosine ratios of acute angles. Use tangents, sines and cosines to find side lengths in right triangles and to solve real-world problems. Geometry Unit J: Trigonometry

Similar Right Triangles
Every right triangle with a given acute angle must be similar. How do we know this is true? The AA Similarity Postulate. Each of these three triangles have two congruent angles which makes them similar. 32° 32° 32° Unit J

Trigonometric Ratios When two right triangles are similar, then the ratios of their sides are the same. In a right triangle, these ratios are called trigonometric ratios. Let’s see a demonstration of these ratios. They are the same for each acute angle. Similar Right Triangles Unit J

The Trigonometric Ratios
Trigonometric ratios are ratios of the sides concerning one acute angle in a right triangle. In this triangle, let’s talk about the ratios for angle A. The side BC is the opposite side (the side directly across from angle A). B AC is the adjacent side AB is the hypotenuse A C Unit J

The Sine Ratio The sine of an angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse. B sin A = c a b A C Unit J

The Cosine Ratio The cosine of an angle is the ratio of the length of the leg adjacent the angle to the length of the hypotenuse. B cos A = c a b A C Unit J

Unit J.1-J.2 Trigonometric Ratios
Tuesday, Feb 28 The Tangent Ratio The tangent of an angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. B tan A = c Insert examples 1 and 2 here. a b A C Unit J Geometry Unit J: Trigonometry

Get Organized: Memory Device
Memory Device for Trigonometric Functions sin = S = cos = C = tan = T = S O H C A H T O A Unit J

Unit J.1-J.2 Trigonometric Ratios Tuesday, Feb 28 Using your graphing calculator You will be using your calculator to find the sine, cosine, or tangent functions. Before you start, you need to make sure that your calculator is set on degrees and not radians. All angles we will be using here are to be in degrees. First push and then make sure that the “degree” is highlighted. To check your calculator, clear screen, push and then “30)”. You should get 0.5 MODE Insert example 3 here SIN Unit J Geometry Unit J: Trigonometry

How do we use this information?
We can use these ratios to find missing measures in a right triangle. B x 40° A C 10 Unit J

Examples of Using Trigonometric Ratios
Unit J.1-J.2 Trigonometric Ratios Tuesday, Feb 28 Examples of Using Trigonometric Ratios To find x, use the sine ratio. To find y, use the cosine ratio. A x 25 Insert examples 4 and 5 here. 63° C y B Unit J Geometry Unit J: Trigonometry