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Warm – up Find the missing measures (go in alphabetical order) x 30° 30 45 60 45 10 z y 60° y x3 3 z 5 3 y 3 2 y5 Trigonometric (trig) Ratios The Trig Functions we will be looking at SINE COSINE TANGENT SINE COSINE TANGENT Greek Letter q Prounounced “theta” Represents an unknown angle Opposite side The side across the triangle from the angle in question opposite q Adjacent side The side next to the angle in question q adjacent Opp Sin Hyp hypotenuse Adj Cos Hyp Opp Tan Adj 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 Or there’s the famous Indian Chief, Chief SOH CAH TOA Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj Finding sin, cos, and tan of an angle. Just writing a ratio Find the sine, the cosine, and the tangent of angle A. 9 opp sin A 10.8 hyp 10.8 9 A adj 6 cos A hyp 10.8 6 Shrink yourself down and stand where the angle is. opp tan A adj Now, figure out your ratios. 9 6 Find the sine, the cosine, and the tangent of angle A A 24.5 8.2 23.1 Shrink yourself down and stand where the angle is. 23.1 opp sin A 24.5 hyp adj cos A hyp 8.2 24.5 opp tan A adj 23.1 8.2 Now, figure out your ratios. Finding an angle. Figure out which ratio to use Use the 2nd button with one of the trig buttons Ex. 1: Find q. Round to one decimal place. nd 2 17.2 q 9 17.2 tan q 9 tan 17.2 9 q 62.4 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 one decimal place. 7 q 23 nd 2 7 cos q 23 cos 7 23 q 72.3 Make sure you are in degree mode (not radians). ) Ex. 3: Find q. Round to one decimal place. q 200 sin q 400 200 nd 2 sin 200 400 ) q 30 Make sure you are in degree mode (not radians).