Solving Trigonometric Equations Solving Trigonometric Equations To solve
![Solving Trigonometric Equations Solving Trigonometric Equations](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-1.jpg)
![Solving Trigonometric Equations To solve trigonometric equations: Use standard algebraic techniques. Look for factoring Solving Trigonometric Equations To solve trigonometric equations: Use standard algebraic techniques. Look for factoring](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-2.jpg)
![Solving Trigonometric Equations For all problems, The solution interval Will be (0, 2 ) Solving Trigonometric Equations For all problems, The solution interval Will be (0, 2 )](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-3.jpg)
![Solving Trigonometric Equations Solve: Step 1: Isosolate cos x using algebraic skills. Step 2: Solving Trigonometric Equations Solve: Step 1: Isosolate cos x using algebraic skills. Step 2:](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-4.jpg)
![Solving Trigonometric Equations Solve: Step 1: Note: Since there is a , all four Solving Trigonometric Equations Solve: Step 1: Note: Since there is a , all four](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-5.jpg)
![Solving Trigonometric Equations Solve: Step 1: Step 2: Note: There is no solution here Solving Trigonometric Equations Solve: Step 1: Step 2: Note: There is no solution here](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-6.jpg)
![Solving Trigonometric Equations Try these: 1. 2. 3. Solution Solving Trigonometric Equations Try these: 1. 2. 3. Solution](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-7.jpg)
![Solving Trigonometric Equations Solve: Factor the quadratic equation. Set each factor equal to zero. Solving Trigonometric Equations Solve: Factor the quadratic equation. Set each factor equal to zero.](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-8.jpg)
![Solving Trigonometric Equations Solve: Replace sin 2 x with 1 -cos 2 x Distribute Solving Trigonometric Equations Solve: Replace sin 2 x with 1 -cos 2 x Distribute](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-9.jpg)
![Solving Trigonometric Equations Solve: Square both sides of the equation in order to change Solving Trigonometric Equations Solve: Square both sides of the equation in order to change](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-10.jpg)
![Solving Trigonometric Equations Solve: Solution: No algebraic work needs to be done because cosine Solving Trigonometric Equations Solve: Solution: No algebraic work needs to be done because cosine](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-11.jpg)
![Solving Trigonometric Equations The solutions still do not exceed 2. Return to 3 x Solving Trigonometric Equations The solutions still do not exceed 2. Return to 3 x](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-12.jpg)
- Slides: 12
![Solving Trigonometric Equations Solving Trigonometric Equations](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-1.jpg)
Solving Trigonometric Equations
![Solving Trigonometric Equations To solve trigonometric equations Use standard algebraic techniques Look for factoring Solving Trigonometric Equations To solve trigonometric equations: Use standard algebraic techniques. Look for factoring](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-2.jpg)
Solving Trigonometric Equations To solve trigonometric equations: Use standard algebraic techniques. Look for factoring and collecting like terms. Isolate the trig function in the equation. Use the inverse trig functions to assist in determining solutions.
![Solving Trigonometric Equations For all problems The solution interval Will be 0 2 Solving Trigonometric Equations For all problems, The solution interval Will be (0, 2 )](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-3.jpg)
Solving Trigonometric Equations For all problems, The solution interval Will be (0, 2 )
![Solving Trigonometric Equations Solve Step 1 Isosolate cos x using algebraic skills Step 2 Solving Trigonometric Equations Solve: Step 1: Isosolate cos x using algebraic skills. Step 2:](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-4.jpg)
Solving Trigonometric Equations Solve: Step 1: Isosolate cos x using algebraic skills. Step 2: Determine in which quadrants cosine is positive. Use the inverse function to assist by finding the angle in Quad I first. Then use that angle as the reference angle for the other quadrant(s). QI QIV Note: cosine is positive in Quad I and Quad IV. Note: The reference angle is /3.
![Solving Trigonometric Equations Solve Step 1 Note Since there is a all four Solving Trigonometric Equations Solve: Step 1: Note: Since there is a , all four](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-5.jpg)
Solving Trigonometric Equations Solve: Step 1: Note: Since there is a , all four quadrants hold a solution with /4 being the reference angle. Step 2: Q 1 QIII QIV
![Solving Trigonometric Equations Solve Step 1 Step 2 Note There is no solution here Solving Trigonometric Equations Solve: Step 1: Step 2: Note: There is no solution here](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-6.jpg)
Solving Trigonometric Equations Solve: Step 1: Step 2: Note: There is no solution here because 2 lies outside the range for cosine.
![Solving Trigonometric Equations Try these 1 2 3 Solution Solving Trigonometric Equations Try these: 1. 2. 3. Solution](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-7.jpg)
Solving Trigonometric Equations Try these: 1. 2. 3. Solution
![Solving Trigonometric Equations Solve Factor the quadratic equation Set each factor equal to zero Solving Trigonometric Equations Solve: Factor the quadratic equation. Set each factor equal to zero.](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-8.jpg)
Solving Trigonometric Equations Solve: Factor the quadratic equation. Set each factor equal to zero. Solve for sin x Determine the correct quadrants for the solution(s).
![Solving Trigonometric Equations Solve Replace sin 2 x with 1 cos 2 x Distribute Solving Trigonometric Equations Solve: Replace sin 2 x with 1 -cos 2 x Distribute](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-9.jpg)
Solving Trigonometric Equations Solve: Replace sin 2 x with 1 -cos 2 x Distribute Combine like terms. Multiply through by – 1. Factor. Set each factor equal to zero. Solve for cos x. Determine the solution(s).
![Solving Trigonometric Equations Solve Square both sides of the equation in order to change Solving Trigonometric Equations Solve: Square both sides of the equation in order to change](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-10.jpg)
Solving Trigonometric Equations Solve: Square both sides of the equation in order to change sine into terms of cosine giving only one trig function to work with. FOIL or Double Distribute Replace sin 2 x with 1 – cos 2 x Set equation equal to zero since it is a quadratic equation. Factor Set each factor equal to zero. Solve for cos x X Why is 3 /2 removed as a solution? Determine the solution(s). It is removed because it does not check in the original equation.
![Solving Trigonometric Equations Solve Solution No algebraic work needs to be done because cosine Solving Trigonometric Equations Solve: Solution: No algebraic work needs to be done because cosine](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-11.jpg)
Solving Trigonometric Equations Solve: Solution: No algebraic work needs to be done because cosine is already by itself. Remember, 3 x refers to an angle and one cannot divide by 3 because it is cos 3 x which equals ½. Since 3 x refers to an angle, find the angles whose cosine value is ½. Now divide by 3 because it is angle equaling angle. Notice the solutions do not exceed 2. Therefore, more solutions may exist. Return to the step where you have 3 x equaling the two angles and find coterminal angles for those two. Divide those two new angles by 3.
![Solving Trigonometric Equations The solutions still do not exceed 2 Return to 3 x Solving Trigonometric Equations The solutions still do not exceed 2. Return to 3 x](https://slidetodoc.com/presentation_image_h2/55c4d4beb683ca86bf48af7c5c92b7dd/image-12.jpg)
Solving Trigonometric Equations The solutions still do not exceed 2. Return to 3 x and find two more coterminal angles. Divide those two new angles by 3. Notice that 19 /9 now exceeds 2 and is not part of the solution. Therefore the solution to cos 3 x = ½ is
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