1 Trigonometric Ratios A RATIO is a comparison of two numbers. For example boys to girls cats dogs right wrong. In Trigonometry the comparison is between sides of a triangle. 2 We need to do some housekeeping before we can proceed 3 In trigonometry the ratio we are talking about is the comparison of the sides of a RIGHT TRIANGLE. Two things MUST BE understood 1. This is the hypotenuse.. This will ALWAYS be the hypotenuse 2. This is 90 this makes the right triangle a right triangle. Without it we can not do this trig we WILL NOT use it in our calculations because we COULD NOT do calculations without it. 4 Now that we agree about the hypotenuse and right angle there are only 4 things left the 2 other angles and the 2 other sides. If we look at angle A there is one side that is adjacent to it and the other side is opposite from it and of course we have the hypotenuse. A We will refer to the sides in terms of their proximity to the angle hypotenuse adjacent opposite 5 If we look at angle B there is one side that is adjacent to it and the other side is opposite from it and of course we have the hypotenuse. hypotenuse opposite B adjacent 6
Remember we wont use the right angle
X 7 One more thing 8 Here we go!!!! 9 Trigonometric Ratios 10 O S sin opposite side hypotenuse H A C cos adjacent side hypotenuse H O T tan opposite side adjacent side A SOH CAH TOA 11 Lets practice Write the ratio for sin A Sin A a c Write the ratio for cos A Cos A b c Write the ratio for tan A Tan A a b B c a C b A Lets switch angles Find the sin cos and tan for Angle B Tan B b a
Sin B b c Cos B a c
12 Make sure you have a calculator Set your calculator to Degree.. MODE (next to 2nd button) Degree (third line down highlight it) 2nd Quit 13 Lets practice Find an angle that has a tangent (ratio) of 2 3 Round your answer to the nearest degree. C 2cm B 3cm A Process I want to find an ANGLE I was given the sides (ratio) Tangent is opp adj TAN-1(2/3) 34 14 Practice some more Find tan A 24.19 12 A 21 Tan A opp/adj 12/21 Tan A .5714 Find tan A 8 Tan A 8/4 2 15 Ok weve found side lengths now lets find angle measures. Refer to your table what function will we use to find angle measures SIN-1 COS-1 TAN-1 These are called INVERSE FUNCTIONS 16 Your assignment
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