Lesson 36 Quadratic Trigonometric Equations Pre Calculus 212022
![Lesson 36 – Quadratic Trigonometric Equations Pre. Calculus 2/1/2022 Pre. Calculus 1 Lesson 36 – Quadratic Trigonometric Equations Pre. Calculus 2/1/2022 Pre. Calculus 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-1.jpg)
![FAST FIVE Solve each equation by factoring n n Solve the quadratic equation x FAST FIVE Solve each equation by factoring n n Solve the quadratic equation x](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-2.jpg)
![(A) Prerequisite Skill: Factoring with Trig n Factor the following trig expressions: 2/1/2022 Pre. (A) Prerequisite Skill: Factoring with Trig n Factor the following trig expressions: 2/1/2022 Pre.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-3.jpg)
![(B) Solving Quadratic Trigonometric Equations n We will outline a process by which we (B) Solving Quadratic Trigonometric Equations n We will outline a process by which we](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-4.jpg)
![(B) Solving Quadratic Trigonometric Equations 2/1/2022 Pre. Calculus 5 (B) Solving Quadratic Trigonometric Equations 2/1/2022 Pre. Calculus 5](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-5.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve sin 2 x – 1 = 0 (B) Solving Quadratic Trigonometric Equations n Solve sin 2 x – 1 = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-6.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve the equation 2 cos 2 x – (B) Solving Quadratic Trigonometric Equations n Solve the equation 2 cos 2 x –](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-7.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve the equation 8 sin 2 x + (B) Solving Quadratic Trigonometric Equations n Solve the equation 8 sin 2 x +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-8.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0°](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-9.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0°](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-10.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ – 45°) = 1 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ – 45°) = 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-11.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ + π/3) = 1 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ + π/3) = 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-12.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 (B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-13.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 (B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-14.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve cos 2(2 x) + 2 cos(2 x) (B) Solving Quadratic Trigonometric Equations n Solve cos 2(2 x) + 2 cos(2 x)](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-15.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-16.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-17.jpg)
![(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(2 x - 2π/3) - (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(2 x - 2π/3) -](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-18.jpg)
![(C) Further Examples n Solve the following without a calculator 2/1/2022 Pre. Calculus 19 (C) Further Examples n Solve the following without a calculator 2/1/2022 Pre. Calculus 19](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-19.jpg)
![(C) Further Examples n Solve the following algebraically, without a GRAPHICAL approach 2/1/2022 Pre. (C) Further Examples n Solve the following algebraically, without a GRAPHICAL approach 2/1/2022 Pre.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-20.jpg)
![(D) Homework n Nelson Textbook, Chap 6. 6 n http: //mrsantowski. tripod. com/2010 Math. (D) Homework n Nelson Textbook, Chap 6. 6 n http: //mrsantowski. tripod. com/2010 Math.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-21.jpg)
- Slides: 21
![Lesson 36 Quadratic Trigonometric Equations Pre Calculus 212022 Pre Calculus 1 Lesson 36 – Quadratic Trigonometric Equations Pre. Calculus 2/1/2022 Pre. Calculus 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-1.jpg)
Lesson 36 – Quadratic Trigonometric Equations Pre. Calculus 2/1/2022 Pre. Calculus 1
![FAST FIVE Solve each equation by factoring n n Solve the quadratic equation x FAST FIVE Solve each equation by factoring n n Solve the quadratic equation x](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-2.jpg)
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 2/1/2022 Pre. Calculus 2
![A Prerequisite Skill Factoring with Trig n Factor the following trig expressions 212022 Pre (A) Prerequisite Skill: Factoring with Trig n Factor the following trig expressions: 2/1/2022 Pre.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-3.jpg)
(A) Prerequisite Skill: Factoring with Trig n Factor the following trig expressions: 2/1/2022 Pre. Calculus 3
![B Solving Quadratic Trigonometric Equations n We will outline a process by which we (B) Solving Quadratic Trigonometric Equations n We will outline a process by which we](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-4.jpg)
(B) Solving Quadratic Trigonometric Equations n We will outline a process by which we come up with the solution to a trigonometric equation ANALYTICALLY using ALGEBRA n We will outline a process by which we come up with the solution to a trigonometric equation GRAPHICALLY using ALGEBRA n it is important you understand WHY we carry out these steps, rather than simply memorizing them and simply repeating them on a test of quiz 2/1/2022 Pre. Calculus 4
![B Solving Quadratic Trigonometric Equations 212022 Pre Calculus 5 (B) Solving Quadratic Trigonometric Equations 2/1/2022 Pre. Calculus 5](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-5.jpg)
(B) Solving Quadratic Trigonometric Equations 2/1/2022 Pre. Calculus 5
![B Solving Quadratic Trigonometric Equations n Solve sin 2 x 1 0 (B) Solving Quadratic Trigonometric Equations n Solve sin 2 x – 1 = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-6.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve sin 2 x – 1 = 0 on the domain 0 < x < 4π. n Your first solution will be analytical. n We will VERIFY with a graphic solution 2/1/2022 Pre. Calculus 6
![B Solving Quadratic Trigonometric Equations n Solve the equation 2 cos 2 x (B) Solving Quadratic Trigonometric Equations n Solve the equation 2 cos 2 x –](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-7.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve the equation 2 cos 2 x – 1 = -cosx on the domain 0 < x < 4π. n Your first solution will be analytical. n We will VERIFY with a graphic solution 2/1/2022 Pre. Calculus 7
![B Solving Quadratic Trigonometric Equations n Solve the equation 8 sin 2 x (B) Solving Quadratic Trigonometric Equations n Solve the equation 8 sin 2 x +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-8.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve the equation 8 sin 2 x + 13 sinx = 4 – 4 sin 2 x on the domain - π < x < 3π. n Your first solution will be analytical. n We will VERIFY with a graphic solution 2/1/2022 Pre. Calculus 8
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2θ 1 if 0 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0°](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-9.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° < θ < 360 ° 2/1/2022 Pre. Calculus 9
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2θ 1 if 0 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0°](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-10.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ) = 1 if 0° < θ < 360 ° 2/1/2022 Pre. Calculus 10
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2θ 45 1 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ – 45°) = 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-11.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ – 45°) = 1 if 0° < θ < 360 ° 2/1/2022 Pre. Calculus 11
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2θ π3 1 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ + π/3) = 1](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-12.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(θ + π/3) = 1 if -2π < θ < 5π 2/1/2022 Pre. Calculus 12
![B Solving Quadratic Trigonometric Equations n Solve cos 2x 2 cosx 0 (B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-13.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 for 0 < x < 2π 2/1/2022 Pre. Calculus 13
![B Solving Quadratic Trigonometric Equations n Solve cos 2x 2 cosx 0 (B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-14.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(x) + 2 cos(x) = 0 for 0 < x < 2π 2/1/2022 Pre. Calculus 14
![B Solving Quadratic Trigonometric Equations n Solve cos 22 x 2 cos2 x (B) Solving Quadratic Trigonometric Equations n Solve cos 2(2 x) + 2 cos(2 x)](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-15.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve cos 2(2 x) + 2 cos(2 x) = 0 for 0 < x < 2π 2/1/2022 Pre. Calculus 15
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2x 3 cosx (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-16.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + 1 = 0 for 0 < x < 2π 2/1/2022 Pre. Calculus 16
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 2x 3 cosx (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) +](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-17.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(x) - 3 cos(x) + 1 = 0 for 0 < x < 2π 2/1/2022 Pre. Calculus 17
![B Solving Quadratic Trigonometric Equations n Solve 2 cos 22 x 2π3 (B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(2 x - 2π/3) -](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-18.jpg)
(B) Solving Quadratic Trigonometric Equations n Solve 2 cos 2(2 x - 2π/3) - 3 cos(2 x - 2π/3) + 1 = 0 for xεR 2/1/2022 Pre. Calculus 18
![C Further Examples n Solve the following without a calculator 212022 Pre Calculus 19 (C) Further Examples n Solve the following without a calculator 2/1/2022 Pre. Calculus 19](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-19.jpg)
(C) Further Examples n Solve the following without a calculator 2/1/2022 Pre. Calculus 19
![C Further Examples n Solve the following algebraically without a GRAPHICAL approach 212022 Pre (C) Further Examples n Solve the following algebraically, without a GRAPHICAL approach 2/1/2022 Pre.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-20.jpg)
(C) Further Examples n Solve the following algebraically, without a GRAPHICAL approach 2/1/2022 Pre. Calculus 20
![D Homework n Nelson Textbook Chap 6 6 n http mrsantowski tripod com2010 Math (D) Homework n Nelson Textbook, Chap 6. 6 n http: //mrsantowski. tripod. com/2010 Math.](https://slidetodoc.com/presentation_image_h2/9da63f0206463a60e96dba65de720e27/image-21.jpg)
(D) Homework n Nelson Textbook, Chap 6. 6 n http: //mrsantowski. tripod. com/2010 Math. SLY 1/Ass essments/Nelson. S 66 p 541. pdf 2/1/2022 Pre. Calculus 21
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