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Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry GOALS: 1. Understand and use the Pythagorean Theorum 2. Define trig functions for a right triangle: soh cah toa 3. Find values of all the trig functions for a triangle, given any 2 parts of the triangle. 4. Learn how to recognize the special triangles: 30 ,60 ,90 45 ,45 ,90 5. Evaluate the special trianges using: sin 30 = 1/2 tan 45 = 1 6. Find trig functions of an angle given another trig funct 7. Learn the Pythagorian Identities; use to simplify Study 5.2 CVC # 17; # 1, 3, 7 13, 17 31; 37, 39, 45, 49, 51, 55, 59, 63, 65, 73 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry Pythagorean Theorum: c2 = a2 + b2 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 1 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry Definitions of Trig. Functions sin θ = y r cos θ = x r tan θ = y x r y θ csc θ = r y sec θ = r x cot θ = x y x Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry Definitions of Trig. Functions sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y Definitions of Trig. Functions sinθ = opp hyp cosθ = adj hyp tanθ = opp adj SOH CAH TOA θ Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 2 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry G: Right Triangle below F: value of all 6 trig functions 6 θ SOH CAH TOA 8 sin θ = csc θ = Definitions of Trig. Functions cos θ = sec θ = cot θ = sinθ = opp hyp cosθ = adj hyp tanθ = opp adj tan θ = SOH CAH TOA Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry G: Right Triangle below F: value of all 6 trig functions 6 SOH CAH TOA θ 8 Definitions of Trig. Functions sinθ = opp hyp cosθ = adj hyp tanθ = opp adj sin θ = csc θ = cos θ = sec θ = cot θ = tan θ = SOH CAH TOA Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 3 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry SOH CAH TOA G: Right Triangle below F: value of all 6 trig functions 41 θ 40 Definitions of Trig. Functions sinθ = opp hyp cosθ = adj hyp tanθ = opp adj sin θ = csc θ = cos θ = sec θ = cot θ = tan θ = SOH CAH TOA Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry G: Right Triangle below F: value of all 6 trig functions 41 θ 40 Definitions of Trig. Functions sinθ = opp hyp cosθ = adj hyp tanθ = opp adj SOH CAH TOA SOH CAH TOA sin θ = csc θ = cos θ = sec θ = cot θ = tan θ = Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 4 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry Special Triangle: 30 , 60 , 90 60 1 2 30 90 √3 sin 30 = 1 2 cos 30 = √3 2 cos 60 = 1 2 sin 60 = √3 2 tan 30 = 1 √3 tan 60 = √3 SOH CAH TOA Definitions of Trig. Functions sin θ = y r cos θ = x r tan θ = y x Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework csc θ = r y sec θ = r x cot θ = x y θ 5.2 Right Triangle Trigonometry Special Triangle: 30 , 60 , 90 60 1 2 30 90 √3 sin 30 = 1 2 cos 30 = √3 2 cos 60 = 1 2 sin 60 = √3 2 tan 30 = 1 √3 tan 60 = √3 SOH CAH TOA Definitions of Trig. Functions Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y θ © G. Battaly 2016 5 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry Special Triangle: 30 , 60 , 90 60 2 1 30 90 √3 sin 30 = 1 2 cos 30 = √3 2 cos 60 = 1 2 sin 60 = √3 2 tan 30 = 1 √3 tan 60 = √3 SOH CAH TOA Definitions of Trig. Functions Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y θ 5.2 Right Triangle Trigonometry Special Triangle: 45 , 45 , 90 sin 45 = 1 √2 cos 45 = 1 √2 45 √2 1 45 tan 45 = 1 1 SOH CAH TOA Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework Definitions of Trig. Functions sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y θ © G. Battaly 2016 6 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry Special Triangle: 45 , 45 , 90 sin 45 = 1 √2 cos 45 = 1 √2 45 √2 1 tan 45 = 1 45 1 SOH CAH TOA Definitions of Trig. Functions Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y θ 5.2 Right Triangle Trigonometry Special Triangle: 45 , 45 , 90 sin 45 = 1 √2 cos 45 = 1 √2 45 √2 1 45 1 tan 45 = 1 SOH CAH TOA Definitions of Trig. Functions Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework sin θ = y r cos θ = x r tan θ = y x csc θ = r y sec θ = r x cot θ = x y θ © G. Battaly 2016 7 Right Triangle Trigonometry G. Battaly November 30, 2016 SOH CAH TOA 5.2 Right Triangle Trigonometry Evaluate: tan π + csc π 4 6 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework SOH CAH TOA 5.2 Right Triangle Trigonometry Evaluate: tan π + csc π 4 6 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 8 Right Triangle Trigonometry G. Battaly November 30, 2016 SOH CAH TOA 5.2 Right Triangle Trigonometry G: sin θ = √21 F: cos θ 5 θ Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework SOH CAH TOA 5.2 Right Triangle Trigonometry G: sin θ = √21 F: cos θ 5 θ Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 9 Right Triangle Trigonometry G. Battaly November 30, 2016 SOH CAH TOA 5.2 Right Triangle Trigonometry Check on calc: G: sin θ = √21 F: cos θ 5 radian mode θ degree mode Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry Pythagorean Theorum: c2 = a2 + b2 c2 = a2 + b2 c2 c2 c2 1 = (sin θ)2 + (cos θ)2 1 = sin2 θ + cos2 θ Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 10 Right Triangle Trigonometry G. Battaly November 30, 2016 5.2 Right Triangle Trigonometry Pythagorean Identity: sin2 θ + cos2 θ = 1 Can this identity be used to generate other identities involving tan θ, sec θ, csc θ, cot θ ? Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page Homework 5.2 Right Triangle Trigonometry Pythagorean Identities: sin2 θ + cos2 θ = 1 sin2 θ + cos2 θ = 1 cos2 θ cos2 θ cos2 θ tan2 θ + 1 = sec2 θ sin2 θ + cos2 θ = 1 sin2 θ sin2 θ sin2 θ 1 + cot2 θ = csc2 θ Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 11 Right Triangle Trigonometry G. Battaly 5.2 Right Triangle Trigonometry Evaluate: sin2 π + cos2 π 10 10 November 30, 2016 Pythagorean Identities: sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ Evaluate: csc2 63 cot2 63 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page 5.2 Right Triangle Trigonometry Evaluate: sin2 π + cos2 π 10 10 Homework Pythagorean Identities: sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ Evaluate: csc2 63 cot2 63 cot2 63 Class Notes: Prof. G. Battaly, Westchester Community College, NY College Algebra & Trig Home Page © G. Battaly 2016 Homework 12 Attachments basic_angles.mp4 trig_functions_unitCircle.mp4
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