Transcript SohCahToa
Designed by: • Emily Freeman McEachern High School 2400 New Macland Rd Powder Springs, GA 30127 Session 17 Warm – up: Find the missing measures. Write all answers in radical form. 45° 30° x 7 10 z 45° w 60° y 13.4 & 13.5 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 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 Finding sin, cos, and tan SOHCAHTOA Opp 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 cosq 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 Finding a side Ex. 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 ? 71.5° 50 y tan 71.5° 50 y = 50 (tan 71.5°) y = 50 (2.98868) y 149.4 ft Ex. 5 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