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Page 1 of 4 College Algebra Unit 9 Review Plan Trig (Geometry Text Chapter 9) Jan 2015 By the end of the 2 week unit a student should be able to: Chapter 9 1) Be able to Utilize the GEOMETRIC MEAN to find missing sides of RIGHT Triangles. 2) Utilize RATIO’s to find missing Sides of Right Triangles 3) Utilize Pythagorean Theorem to find missing sides of Right triangles 4) Understand Reference angle: θ is called THETA (Greek letter) for an angle 5) Understand Terminal side and how to measure Positive and Negative Angles 6) Utilize the Unit Circle to find: a) Reference Points b) Reference Angles 7) Know the THREE primary TRIG values for a) 0 deg 30 deg 45 deg b) Sin = 0.000 0.5000 0.7071 c) Cos = 1.000 0.8660 0.7071 d) Tan = 0.000 0.57735 1.0000 60 deg 0.8660 0.5000 1.7321 90 deg 1.0000 0.0000 undefined 8) TRIGONOMETRIC RATIO’s Given a right triangle with one angle and one side a) Find the missing angles and missing side b) A2 + B2 = C2 Adj2 + Opp2 = Hyp2 Hyp c) SIN θ = Opp/ Hyp Opp θ d) COS θ = Adj/ Hyp Adj e) TAN θ = Opp/ Adj SIN (30) = 1/2 (or 0.500) 9) Given a right triangle three sides a) Find the missing angles b) ARCSIN (Opp / Hyp ) = θ c) ARCCOS (Adj / Hyp ) = θ d) ARCTAN (Opp / Adj ) = θ SIN-1 (1/2) = 30 degrees Page 1 of 4 Page 2 of 4 10) Find The area of a RIGHT-Triangle a) BASIC Area = ½ (base) ( Height) Height Base b) OTHER ways to Find Area if NOT a Right Triangle A c Area = ½ bc{SIN (A)} Area = ½ ac{SIN (B)} b B C a 11) HONORS Convert angles in Degree-minutes-seconds into Degrees Decimal i. 30 deg – 15 min – 30 sec ii. 30 deg + 15/60 + 30/3600 = 30 + .25 + 0.01 = 30.2501 degrees 12) HONIORS Find the true inverse trig functions a) 1 /SIN = CSC b) 1 / COS = SEC c) 1 / TAN = COT 13) Utilize the Law of COSINE’s for a NON right Triangle to find a) Find the missing angles and sides In the Triangle find the missing sides and angles A c c = a + b – 2ab*COS C b2 = a2 + c2 – 2ac*COS B a2 = c2 + b2 – 2cb*COS A 2 2 2 b B C a 14) Utilize the Law of SINE’s for a NON right Triangle to find a) Find the missing angles and sides In the Triangle find the missing sides and angles A c SIN (A) / a = SIN (B) / b = SIN (C) / c b B C Page 2 of 4 a Page 3 of 4 Area = ½ ab{SIN (C)} Area = ½ a2 {{SIN (B)* SIN(C)} / SIN(A)} Area = ½ b2 {{SIN (A)* SIN(C)} / SIN(B)} Area = ½ c2 {{SIN (A)* SIN(B)} / SIN(C)} Finally...For ANY triangle with side lengths “a”, “b” and “c” Area = √{s* (s-a) (s-b)(s-c)} Where s = ½ * (a + b + c) Page 3 of 4 Page 4 of 4 HONORS GRAPHING SIN and COS 1) Plot the equations for a SIN or COS function a) f(x) = C + A SIN (Bx) i. C = shift on the “Y” axis = {MAX + MIN} /2 ii. A = Amplitude = {MAX – MIN} /2 iii. B finds the period of the cycle = 2π / B 1. If B = 1 then the “normal” period is 2π 2. (a circles circumference) iv. b = 2π / period v. Graph the quarter periods vi. Graph the MAX vii. Graph the MIN viii. Graph the “C” ix. SIN starts at ZERO x. COS Starts at MAX xi. f = FREQUENCY {Cycles per unit time} = 1 /P = 1 / {2π / B} Graph the equation f(Ψ) = Y = 2 + 4 * SIN ({1/4}Ψ) Graph the equation f(Ψ) = Y = 2 + 4 * COS ({1/4}Ψ) COS MAX +4 (6) EQ MIN EQ 8π* 1/4 2π MAX 8π * 1/2 4π EQ MAX 2 -4 (-2) SIN EQ 8π * 3/4 6π MIN Page 4 of 4 8π PERIOD 8π EQ