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Evaluate and graph reciprocal trigonometric functions by applying rules for trigonometric functions. We know the trigonometric functions: sine, cosine, tangent The reciprocals of these functions have names: 1 = 𝑐𝑠𝑐𝜃 𝑠𝑖𝑛𝜃 1 = 𝑠𝑒𝑐𝜃 𝑐𝑜𝑠𝜃 1 = 𝑐𝑜𝑡𝜃 𝑡𝑎𝑛𝜃 this is the cosecant this is the secant this is the cotangent Find cot(− 5𝜋 ) 6 without using a calculator This is the point (− 3 1 ,− ) 2 2 Since we know that 𝑡𝑎𝑛𝜃 = 3 −2 1 −2 = 3 𝜋 6 You try: find csc( ) 2 on the unit circle 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 = 𝑦 𝑥 then the cotangent must be 𝑐𝑜𝑡𝜃 = 𝑥 𝑦 Make sure you are in radian mode! Find sec(2) Secant is the reciprocal of cosine Type 1/cos(2) Round: sec(2) ≈ -2.403 You try: find cot(10) to the nearest thousandth 1.542 Find csc(35°) You can change to degree mode OR leave in radian mode and type 1/sin(35°) You get the degree symbol by going to the ANGLE menu (above APPS) 1.743 Make a table of values Ex: sketch the graph of 𝑦 = csc 𝑥 from 0 𝑡𝑜 2𝜋 csc is the reciprocal of sin Make a table for the graph of 𝑦 = sin 𝑥 X 0 𝝅 𝟑 Sin(x) 0 0.9 Csc(x) --- 1.2 𝝅 𝟐 1 𝟐𝝅 𝟑 0.9 1 1.2 0 𝟒𝝅 𝟑 -0.9 𝟑𝝅 𝟐 -1 𝟓𝝅 𝟑 -0.9 0 --- -1.2 -1 -1.2 --- 𝝅 Now include values of 𝑦 = csc 𝑥 which are 1 sin 𝑥 Undefined wherever sin(x) = 0 so we have asymptotes 𝟐𝝅 Odds p.888 #9-45