Lesson Objective: Evaluate trig functions.

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Presentation transcript:

Lesson Objective: Evaluate trig functions. 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: Name Func­tion   The 6 Trig Functions: Name Ab­bre­via­­tions Func­tion Func­tions Sine sin y = sin t Cosecant csc csc t = 1/y y ≠ 0 csc t = 1/ Cosine cos x = cos t Secant sec sec t = 1/x x ≠ 0 sec t = 1/ Tangent tan tan t = y/x x ≠ 0 tan t= / Cotangent cot cot t = x/y 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 2 csc π/3 = 1/y = cos π/3 = x = ½ sec π/3 = 1/x = tan π/3 = y/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. t = - 25π 4  sin / = y = csc / = 1/y = cos / = x = sec / = 1/x = tan / = y/x = cot / = x/y =

Lesson 2: Evaluating Trig Functions   Evaluate the six trigonometric functions at each real number. C. t = 29π 2  sin / = y = csc / = 1/y = cos / = x = sec / = 1/x = tan / = y/x = cot / = x/y =

Lesson 3: Domain, Period, Odd and Even Domain: All real numbers – why?   Domain: All real numbers – why? Range: Any idea?

Lesson 3: Domain, Period, Odd and Even Domain: All real numbers   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:   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. csc π 8   Evaluate using a calculator. csc π 8 sin(-100°)

Evaluate the six trigonometric functions at each real number. 4.2: Do I Get It? Yes or No   Evaluate the six trigonometric functions at each real number. t = 13π 6 t = 5π t = - π 3 Evaluate cot 1.5 using a calculator.