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Pre-Calculus 4.3 Trigonometric functions or…Soak your toes in what, now? Welcome to trigonometric function review! Define: sin θ = θ cos θ = tan θ = sec θ = = csc θ = = cot θ = = Trigonometric Functions of Special Right Triangles Fill in the missing leg and hypotenuse. 45˚ In a 45-45-90: Hypotenuse = Find: sin 45˚ = sec 45˚ = 45˚ 1 cos 45˚ = csc 45˚ = tan 45˚ = cot 45˚ = Fill in the missing leg and the hypotenuse In a 30-60-90: 60˚ Hypotenuse = 1 Long leg = Find: sin 30˚ = sec 30˚ = cos 30˚ = csc 30˚ = tan 30˚ = cot 30˚ = sin 60˚ = sec 60˚ = cos 60˚ = csc 60˚ = tan 60˚ = cot 60˚ = 30˚ Trigonometric Identities Cofunction Identities Look at the values of sin 60˚ and cos 30˚. What do you notice? How about sec 30˚ and csc 60˚? This is true for all complementary angles, or to put it another way: sin( 90 ) cos cos(90 ) sin tan( 90 ) cot cot(90 ) tan sec( 90 ) csc csc( 90 ) sec or: Cofunctions of complementary angles are equal. Reciprocal Identities 1 1 sin cos csc sec csc 1 sin Quotient Identities sin tan cos sec 1 cos cot tan 1 cot cot 1 tan cos sin Pythagorean Identities sin 2 cos 2 1 1 tan 2 sec 2 1 cot 2 csc 2 Use the trigonometric identities to find the following: 1) sin 0.6 Find the values of cos and tan . 2) Find sin , cos , cot , csc , and sec if you know that tan = 3. 3) A surveyor stands 50 feet away from a tree. The angle of elevation to the top of the tree is 71.5˚. What is the height of the tree? 4) A twelve meter flagpole casts a 9-meter shadow. Find the angle of elevation to the sun. Assignment:p.387#1-21odds,33-37odds,43,44,47,49,63-69odds