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Find the missing measures. Write all answers in radical form. 45° 30° x 7 10 z 45° w 60° y The Trigonometric Functions we will be looking at SINE COSINE TANGENT The Trigonometric Functions SINE COSINE TANGENT SINE Prounounced “sign” COSINE Prounounced “co-sign” TANGENT Prounounced “tan-gent” Greek Letter q Prounounced “theta” Represents an unknown angle Opp Sinq Hyp hypotenuse Adj Cosq Hyp Opp Tanq 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 Finding sin, cos, and tan SOHCAHTOA Opp Sinq Hyp Adj Cosq Hyp 8 10 4 5 10 8 3 6 10 5 q Opp 8 4 Tanq Adj 6 3 6 Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 9 opp sin A hypo 10.8 .8333 adj 6 cos A hypo 10.8 .5555 6 opp tan A adj 9 6 1.5 Find the values of the three trigonometric functions of q. ? 5 4 q Pythagorean Theorem: (3)² + (4)² = c² 5=c 3 opp 4 adj 3 opp 4 sin q cos q tan q hyp 5 hyp 5 adj 3 Find the sine, the cosine, and the tangent of angle A B Give a fraction and decimal answer (round to 4 decimal places). 24.5 8.2 A 23.1 opp 8.2 sin A .3347 24 . 5 hypo 23.1 adj cos A 24.5 .9429 hypo opp tan A adj 8 .2 23.1 .3550 Let’s find the calculator connections. Draw a 30º-60º-90º to help you find sin 30º. Now use your calculator to find sin 30º. So… What is sin 45º? 1 What is cos 27º? .8910 What is tan 62º? 1.881 Can using the calculator help us solve this problem? In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. Can using the calculator help us solve this problem? In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. Q PR tan35 35 16 16 16 tan35 PR P R PR 11.20 Can using the calculator help us solve this problem? In triangle PQR, m P = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. 16 Q cos35 35 QR 16 QR cos35 16 P R QR 16 cos35 QR 19.53 What about indirect measurement? • The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite actually flying? Solution: • The angle of elevation of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite flying? h sin 79 100 100 sin 79 h 100’ 98.16' 79º h You try…. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? Opp tan 71.5° Hyp x 71.5° 50 x tan 71.5° 50 x = 50 (tan 71.5°) x = 50 (2.98868) x 149.4 ft A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards