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13.1 Use Trigonometry with Right Triangles Right Triangle Trigonometry C b hypotenuse leg a B c leg A Trigonometry Functions: SOH – CAH – TOA O H Sine: sin = /H Cosine: cos = A/H Tangent: tan = O/A Cosecant: csc = /O Secant: sec = H/A Cotangent: cot = A/O Reciprocal Relationships csc = 1/sin sec = 1/cos cot = 1/tan Evaluate the six trigonometric functions for the angle sin = ________ cos = ________ tan = _________ 7 csc = ________ sec = ________ cot = _________ 24 Special Triangles 30 - 60 - 90 B 30 Degrees sin 30 = ______ cos 30 = ______ tan 30 = ______ csc 30 = ______ sec 30 = ______ cot 30 = ______ 30 30 √3 2 2 60 A 60 1 D 1 60 Degrees sin 60 = ______ cos 60 = ______ tan 60 = ______ csc 60 = ______ sec 60 = ______ cot 60 = ______ C A 45 - 45 - 90 45 Degrees 45º √2 1 45º C 1 B sin 45 = _____ cos 45 = _____ tan 45 = _____ csc 45 = _____ sec 45 = _____ cot 45 = _____ Use a right triangle to find the values of all of the trigonometry functions of Given: sin = 1/3 cos = ________ tan = ________ Find an unknown side length of a right triangle Find the exact value for x in the right triangle below. 6 x 45 x = ____________________ Use a calculator to solve a right triangle Solve Triangle ABC. B B = ______________________ c = 20 a = ______________________ a b = ______________________ 54 A b C Angle of elevation From a point on the ground 28 feet from the base of a flagpole, the angle of elevation to the top of the flagpole is 63. Estimate the height of the flagpole.