Lesson 28 Quadratic Trigonometric Equations IB Math HL
Lesson 28 – Quadratic Trigonometric Equations IB Math HL - Santowski 12/22/2021 HL Math 1
FAST FIVE Solve each equation by factoring n n Solve the quadratic equation x 2 + 2 x = 15 algebraically Solve the quadratic equation x 2 + 2 x = 15 graphically 1. (k+1)(k-5) = 0 2. (a+1)(a+2) = 0 3. (4 k+5)(k+1) = 0 4. (2 m+3)(4 m+3) = 0 5. x 2 – 11 x + 19 = -5 6. n 2 + 7 n + 15 = 5 7. n 2 – 10 n + 22 = -2 8. n 2 + 3 n – 12 = 6 9. 6 n 2 – 18 n – 18 = 6 10. 7 r 2 – 14 r = – 7 12/22/2021 HL Math 2
(A) Prerequisite Skill: Factoring with Trig n Factor the following trig expressions: 12/22/2021 HL Math 3
(B) Solving Quadratic Trigonometric Equations 12/22/2021 HL Math 4
(C) Further Examples n Solve the following without a calculator 12/22/2021 HL Math 5
(B) Solving Quadratic Trigonometric Equations n Solve: (a) sin 2 x – 1 = 0 on 0 < x < 4π. (b) 2 cos 2 x – 1 = -cosx on 0 < x < 4π. (c) 8 sin 2 x + 13 sinx = 4 – 4 sin 2 x on -π < x < 3π. n Your first solution will be analytical. n We will VERIFY with a graphic solution n 12/22/2021 HL Math 6
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° < θ < 360 ° 12/22/2021 HL Math 7
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° < θ < 360 ° 12/22/2021 HL Math 8
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ – 45°) = 1 if 0° < θ < 360 ° 12/22/2021 HL Math 9
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ + π/3) = 1 if -2π < θ < 5π 12/22/2021 HL Math 10
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 for 0 < x < 2π 12/22/2021 HL Math 11
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 for 0 < x < 2π 12/22/2021 HL Math 12
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(2 x) + 2 cos(2 x) = 0 for 0 < x < 2π 12/22/2021 HL Math 13
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + 1 = 0 for 0 < x < 2π 12/22/2021 HL Math 14
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + 1 = 0 for 0 < x < 2π 12/22/2021 HL Math 15
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(2 x - 2π/3) - 3 cos(2 x - 2π/3) + 1 = 0 for xεR 12/22/2021 HL Math 16
(C) Double Angle Identities Equations n Solve the following equations, making use of the double angle formulas for key substitutions: 12/22/2021 HL Math - Santowski 17
(B) Solving Other Trigonometric Equations n Solve on xεR: n (a) sin 2(x) – 2 cos(x) = 2 (b) cos(2 x) – 3 sin(x) + 1 = 0 n n (c) Determine the x-coordinates of the intersection points of the function f(x) = cos(2 x) and g(x) = sin 2(x) – sin(x) -1. You are given the fact that sin-1(-2/3) = -0. 73 12/22/2021 HL Math 18
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