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Date: 4.2 Notes: The Unit Circle Lesson Objective: Evaluate trig functions. CCSS: F-TF Extend the domain of trigonometric functions using the unit circle. You will need: calculator This is Jeopardy!: These are the trig inverse functions for sine and cosine. Lesson 1: Trig. Functions The 6 Trig Functions: AbbreName via- Function Name tions Sine sin Abbreviations Functions y = sin t Cosecant csc csc t = 1/y y≠0 Cosine cos x = cos t Secant csc t = 1/ sec sec t = 1/x x≠0 sec t = 1/ Tangent tan tan t = y/x Cotangent cot cot t = x/y x≠0 tan t= / y≠0 cot t= / Lesson 2: Evaluating Trig Functions Evaluate the six trigonometric functions at each real number. A. t = 60° sin π/3 = y = 3 cos π/3 = x = ½ tan π/3 = y/x = 2 csc π/3 = 1/y = sec π/3 = 1/x = cot π/3 = x/y = Lesson 2: Evaluating Trig Functions Lesson 2: Evaluating Trig Functions Evaluate the six trigonometric functions at each real number. B. 25π t=4 sin / = y = cos / = x = tan / = y/x = csc / = 1/y = sec / = 1/x = cot / = x/y = Lesson 2: Evaluating Trig Functions Evaluate the six trigonometric functions at each real number. C. t= 29π 2 sin / = y = cos / = x = tan / = y/x = csc / = 1/y = sec / = 1/x = cot / = x/y = Lesson 3: Domain, Period, Odd and Even Domain: All real numbers – why? Range: Any idea? Lesson 3: Domain, Period, Odd and Even Domain: All real numbers Range: -1 ≤ y ≤ 1 and -1 ≤ x ≤ 1 -1 ≤ sin t ≤ 1 -1 ≤ cos t ≤ 1 Lesson 3: Domain, Period, Odd and Even Period: sin(t + 2πn) = sin t cos(t + 2πn) = cos t Lesson 3: Domain, Period, Odd and Even Lesson 3: Domain, Period, Odd and Even Lesson 4: Using a Calculator Evaluate using a calculator. A. csc π 8 B. sin(-100°) 4.2: Do I Get It? Yes or No Evaluate the six trigonometric functions at each real number. 13π 1. t = 6 2. t = 5π π 3. t = 3 4. Evaluate cot 1.5 using a calculator.