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Solving Trigonometric Equations: Verify Solutions & Find Solutions in the Range

Learn how to verify x-values as solutions and solve for x over the range of 0 < x < 2π in trigonometric equations. Understand the importance of checking the unit circle and solving for each equation factor. Get all trig functions onto one side to simplify the process effectively.

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Solving Trigonometric Equations: Verify Solutions & Find Solutions in the Range

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  1. Chapter 5.3 Solving Trigonometric Equations

  2. Objectives • Verify x-values that are solutions of an equation

  3. Ex: 1 Plug And Chug!Verifying an equation at a given x-value • Given x = π/8, verify that the x-value is the solution of the equation:

  4. Ex: 1 Plug And Chug!Verifying an equation at a given x-value

  5. Ex. 2A: Finding the solutions to an equation • Solve for x over the range of 0 < x < 2π • Get the trig value by itself, or at least as a power of itself

  6. Ex. 2A: Finding the solutions to an equation • Check the unit circle for viable x values

  7. Ex. 2B: Finding the solutions to an equation • Solve for x over the range of 0 < x < 2π • Notice there are two factors, if either factor is 0, then the equation will equal zero • Therefore, you need to solve for each equation

  8. Ex. 2B: Finding the solutions to an equation

  9. Ex. 2C: Finding the solutions to an equation • Solve for x over the range of 0 < x < 2π • Notice there are two trig functions, so pay close attention so you can get them to equal the same trig function

  10. Ex. 2C: Finding the solutions to an equation • Now you can get all the trig functions onto one side.

  11. Ex. 2C: Finding the solutions to an equation • Now you can factor!

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