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Bellwork sin 120o = cos2π = tan3π/2 = ...Study your Unit Circle for Quiz #2 Today! 113 Answers: 1. 3. 5. 7. 9. Sin π/4 = 10. Sin π/4 = Cos π/4 = Cos π/4 = Tan π/4 = Tan π/4 = 11. Sin 5π/4 = Cos 5π/4 = 12. Sin 5π/6 = Cos 5π/6 = Tan 5π/4 = Tan 5π/6 = 13. Sin 11π/6= 14. Sin 2π/3= Cos 11π/6= Cos 2π/3= Tan 11π/6= Tan 2π/3= 15. Sin 4π/3= 16. Sin 7π/4 = Cos 4π/3= Cos 7π/4 = Tan 4π/3= Tan 7π/4 = Notes 114: The SIX Trigonometric Functions You already know the following 3 trig functions represent the sides of the special right triangles in the unit circle. Sine abbreviated: sin Cosine abbreviated: cos and Tangent abbreviated: tan 60 45 You already know the INVERSE for each is 30 What you may not realize is each of these is the reciprocal of: abbreviated: sin1 = Sine abbreviated: cos1 = and abbreviated: tan1 = Cosine and Tangent Now meet: Secant abbreviated: sec = cos1 1 sin Cosecant abbreviated: csc = and 1 tan Cotangent abbreviated: cot = These 3 trig. functions ALSO represent the reciprocal of the one of the first 3 Trig functions... 1 a.k.a. ( sin , , ) can you guess which? :) cos1 tan1 SIX Trigonometric Functions The reciprocal of ... Sine = Cosecant Cosine and Tangent = Secant and = Cotangent How does this affect the coordinates of our circle? Lets look at a chart! Find the Secant of each of the following angles. o 60 90o 0 30 45 0 π/6 π/ 4 π / 3 π / 2 o o o θ: Cosθ Secθ Cosθ "RECIPROCALS" Hint: (Cos1) = (Sec) (Cos, Sin) Cosines and Secants Find the Cosecant of each of the following angles. o o o 0 30 45 60 90o π π π π 0 /6 /4 /3 /2 o θ: Sinθ Cscθ Sinθ "RECIPROCALS" 1 Hint: (Sin ) = (Csc) (Cos, Sin) Sines and Cosecants. Find the Cotangent of each of the following angles. 0 θ: o o o o 30 45 60 90 o Tanθ= sin/cos Cotθ= cos/sin Tanθ "RECIPROCALS" 1 Hint: (Tan ) = (Cot) (Cos, Sin) Tangents and Cotangents Ignore the Denominators! Hint #1: (Cos, Sin) and Tan = Sin/Cos AlphaOrder Hint #2: (Sec, Csc) and Cot = Cos/Sin Reciprocals = Reverse AlphaOrder Note: For COtangent the COsine is on top! Assignment 114 Page 345 #28 even, 1722 all Only 10 problems!!! Please remember to show all your work!