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Math 170 Trigonometry Lecture Notes Chapter 6 6.1 & 6.2 Trigonometric Equations 6.1 Solve using factoring, quadratic formula, or horizontal translations 6.2 Solve using identities, clearing denominators, or squaring both sides [CA – Review problems 6.1 # 77, 79, 81] Basic Concepts for Solving Trigonometric Equations: Goal: To get ONE trig function equal to a number. Method Depends on the Type of Equation: ♦ Quadratics: Factor or Use Quadratic Formula ♦ Two Functions in One Equation: o Try Factoring o Use Pythagorean Identities to Change to One Function (may need to square in order to do this) ♦ Fractions: Clear the denominators by multiplying by LCD ♦ Since Trigonometric Functions are periodic, they repeat. o For sin, cos, csc & sec add ________________ o For tan & cot add ______________ B) Solve. Find the solutions in the interval [0, 2π) 1) (sin x – 1) (sin x + 2) = 0 3) 2) 2 cos2x – cos x = 1 2 tan θ =1 3 − tan 2 θ CA 6.1 11, 19, 33 6.2 #7, 37, 43 1 Math 170 Trigonometry Lecture Notes Chapter 6 Applications: If a projectile is fired into the air with an intial velocity v at an angle of elevation θ, then the height h of the projectile at time t is given by (see picture pg 327, 6.1 problem set) h = -16t2 + v∙t sinθ 6.1 #72 Give the equation for h if v is 600 feet per second and θ is 45o (Leave answer in exact form.) 6.1 #74 Use the equation you found in #72 to find the height of the object after 3 seconds (round solution to the nearest tenth). CA 6.1 #76 2 Math 170 Trigonometry Lecture Notes Chapter 6 6.3 Trigonometric Equations of Multiple Angles Solve the equations: (a) Find all Solutions and (b) Find solutions in the Interval [0, 2π) 1) 3 tan 3 x = 3 2) − 2 cos 2 x = 3 3) cos 2θ – cos θ = 0 CA 6.3 #15, 25, 39 3