Solving Trigonometric Equations First Degree Trigonometric Equations These
![Solving Trigonometric Equations Solving Trigonometric Equations](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-1.jpg)
![First Degree Trigonometric Equations: • These are equations where there is one kind of First Degree Trigonometric Equations: • These are equations where there is one kind of](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-2.jpg)
![Steps for Solving: • Isolate the Trigonometric function. • Use exact values to solve Steps for Solving: • Isolate the Trigonometric function. • Use exact values to solve](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-3.jpg)
![Now figure out where sin = -1/2 on the unit circle. Now figure out where sin = -1/2 on the unit circle.](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-4.jpg)
![Complete the List of Solutions: • If you are not restricted to a specific Complete the List of Solutions: • If you are not restricted to a specific](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-5.jpg)
![Where k is an integer and gives all the coterminal angles of the solution. Where k is an integer and gives all the coterminal angles of the solution.](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-6.jpg)
![Practice • Solve the equation. Find the general solutions Practice • Solve the equation. Find the general solutions](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-7.jpg)
![Second Degree Trigonometric Equations: • These are equations that have one kind of Trigonometric Second Degree Trigonometric Equations: • These are equations that have one kind of Trigonometric](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-8.jpg)
![This is a difference of squares and can factor Solve each factor and you This is a difference of squares and can factor Solve each factor and you](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-9.jpg)
![Practice Find the general solutions for Practice Find the general solutions for](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-10.jpg)
![Writing in terms of 1 trig fnc • If there is more than one Writing in terms of 1 trig fnc • If there is more than one](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-11.jpg)
![Solve the following Replace cos 2 with 1 -sin 2 Solve the following Replace cos 2 with 1 -sin 2](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-12.jpg)
![Solving for Multiple Angles • Multiple angle problems will now have a coefficient on Solving for Multiple Angles • Multiple angle problems will now have a coefficient on](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-13.jpg)
![Find the general solutions for sin 3 x +2= 1 Find the general solutions for sin 3 x +2= 1](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-14.jpg)
![Practice Practice](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-15.jpg)
- Slides: 15
![Solving Trigonometric Equations Solving Trigonometric Equations](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-1.jpg)
Solving Trigonometric Equations
![First Degree Trigonometric Equations These are equations where there is one kind of First Degree Trigonometric Equations: • These are equations where there is one kind of](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-2.jpg)
First Degree Trigonometric Equations: • These are equations where there is one kind of trig function in the equation and that function is raised to the first power.
![Steps for Solving Isolate the Trigonometric function Use exact values to solve Steps for Solving: • Isolate the Trigonometric function. • Use exact values to solve](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-3.jpg)
Steps for Solving: • Isolate the Trigonometric function. • Use exact values to solve and put answers in terms of radians. • If the answer is not an exact value, then use inverse functions on your calculator to get answers
![Now figure out where sin 12 on the unit circle Now figure out where sin = -1/2 on the unit circle.](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-4.jpg)
Now figure out where sin = -1/2 on the unit circle.
![Complete the List of Solutions If you are not restricted to a specific Complete the List of Solutions: • If you are not restricted to a specific](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-5.jpg)
Complete the List of Solutions: • If you are not restricted to a specific interval and are asked to give the general solutions then remember that adding on any integer multiple of 2π represents a coterminal angle with the equivalent trigonometric ratio.
![Where k is an integer and gives all the coterminal angles of the solution Where k is an integer and gives all the coterminal angles of the solution.](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-6.jpg)
Where k is an integer and gives all the coterminal angles of the solution.
![Practice Solve the equation Find the general solutions Practice • Solve the equation. Find the general solutions](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-7.jpg)
Practice • Solve the equation. Find the general solutions
![Second Degree Trigonometric Equations These are equations that have one kind of Trigonometric Second Degree Trigonometric Equations: • These are equations that have one kind of Trigonometric](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-8.jpg)
Second Degree Trigonometric Equations: • These are equations that have one kind of Trigonometric function that is squared in the problem. • We treat these like quadratic equations and attempt to factor or we can use the quadratic formula.
![This is a difference of squares and can factor Solve each factor and you This is a difference of squares and can factor Solve each factor and you](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-9.jpg)
This is a difference of squares and can factor Solve each factor and you should end up with 4 solutions
![Practice Find the general solutions for Practice Find the general solutions for](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-10.jpg)
Practice Find the general solutions for
![Writing in terms of 1 trig fnc If there is more than one Writing in terms of 1 trig fnc • If there is more than one](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-11.jpg)
Writing in terms of 1 trig fnc • If there is more than one trig function involved in the problem, then use your identities. • Replace one of the trig functions with an identity so there is only one trig function being used
![Solve the following Replace cos 2 with 1 sin 2 Solve the following Replace cos 2 with 1 -sin 2](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-12.jpg)
Solve the following Replace cos 2 with 1 -sin 2
![Solving for Multiple Angles Multiple angle problems will now have a coefficient on Solving for Multiple Angles • Multiple angle problems will now have a coefficient on](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-13.jpg)
Solving for Multiple Angles • Multiple angle problems will now have a coefficient on the x, such as sin 2 x=1 • Solve the same way as previous problems, but divide answers by the coefficient • For general solutions divide 2 by the coefficient for sin and cos. Divide by the coefficient for tan and cot.
![Find the general solutions for sin 3 x 2 1 Find the general solutions for sin 3 x +2= 1](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-14.jpg)
Find the general solutions for sin 3 x +2= 1
![Practice Practice](https://slidetodoc.com/presentation_image_h2/91aeb64c5645be0eec6045b870982f9c/image-15.jpg)
Practice
Isosolate
5-3 solving trigonometric equations
Solving linear trigonometric equations
5-3 solving trigonometric equations
Third degree polynomial equation
Inverse circular functions and trigonometric equations
Tan 240⁰
What is the value of sin 30ᵒ?
How to solve trigonometric equations step by step
Trig equations
Mark up rule
Soldering iron for clothes
First degree burn
Circuit theory
Unit 5 polynomial functions homework 2
Essential questions for quadratic functions