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The Trigonometric Functions we will be looking at SINE COSINE TANGENT The Trigonometric Functions SINE COSINE TANGENT SINE Pronounced “sign” COSINE Pronounced “co-sign” TANGENT Pronounced “tan-gent” Greek Letter q Prounounced “theta” Represents an unknown angle Opp Leg Sin Hyp Adj Leg Cos Hyp Opp Leg Tan Adj Leg hypotenuse q adjacent opposite opposite We need a way to remember all of these ratios… Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment SOHCAHTOA Old Hippie Sin Opp Hyp Cos Adj Hyp Tan Opp Adj Finding sin, cos, and tan. (Just writing a ratio or decimal.) Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 9 opp sin A 10.8 .8333 hyp 10.8 9 A adj 6 cos A hyp 10.8 .5556 6 Shrink yourself down and stand where the angle is. opp tan A adj Now, figure out your ratios. 9 6 1.5 Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). 24.5 8.2 A 23.1 Shrink yourself down and stand where the angle is. 8 .2 opp sin A . 3347 24.5 hyp adj cos A hyp 23.1 24.5 .9429 opp tan A adj 8 .2 23.1 .3550 Now, figure out your ratios. Finding a side. (Figuring out which ratio to use and getting to use a trig button.) Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. x tan 55 20 20 m 55 20 tan 55 x 20 tan 55 ) x 28.6 m x Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. Ex: 2 Find the missing side. Round to the nearest 80 tan 72 x x tan 72 80 tenth. 80 ft 80 x tan 72 72 x 80 ( tan Shrink yourself down and stand where the angle is. 72 ) ) = x 26 ft Now, figure out which trig ratio you have and set up the problem. Ex: 3 Find the missing side. Round to the nearest tenth. x 283 m 24 Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. x sin 24 283 283sin 24 x x 115.1 m Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft 40 x x cos40 20 20 cos40 x x 15.3 ft Finding an angle. (Figuring out which ratio to use and getting to use the 2nd button and one of the trig buttons.) Ex. 1: Find q. Round to four decimal places. nd 2 17.2 q 9 17.2 tan q 9 tan 17.2 9 ) q 62.3789 Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. Make sure you are in degree mode (not radians). Ex. 2: Find q. Round to three decimal places. 7 q 23 nd 2 7 cos q 23 cos 7 23 q 72.281 Make sure you are in degree mode (not radians). ) Ex. 3: Find q. Round to three decimal places. q 200 sin q 400 200 nd 2 sin 200 400 ) q 30 Make sure you are in degree mode (not radians). When we are trying to find a side we use sin, cos, or tan. When we are trying to find an angle we use sin-1, cos-1, or tan-1.