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Solving Trigonometric Equations

Learn how to solve trigonometric equations by isolating the trigonometric function and using algebraic techniques like factoring and extracting square roots.

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Solving Trigonometric Equations

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  1. Chapter 5.3

  2. Give an algebraic expression that represents the sequence of numbers. Let n be the natural numbers (1, 2, 3, …). 2, 4, 6, … 1, 3, 5, … 7, 10, 13, 16, … 9, 14, 19, 24, … …45,135,225,315,… …60,120,240,300,…

  3. 5.3 Solving Trigonometric Equations In this chapter you will be learning how to solve trigonometric equations To solve a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation. In other words, get the trigonometric function to one side by itself. Use standard algebra such as collecting like terms and factoring to do this.

  4. 5.3 Solving Trigonometric Equations For Example: Original equation Add 1 to each side Divide each side by 2 To solve for x, note that the equation has the solutions and in the interval . Remember that since has a period of , there are infinitely many other solutions that can be written as: and General solution

  5. 5.3 Solving Trigonometric Equations The equation has infinitely many solutions. Any angles that are coterminal with are also solutions to the equation.

  6. 5.3 Solving Trigonometric Equations Collecting like terms Find all of the solutions of in the interval The solutions in the interval are and

  7. 5.3 Solving Trigonometric Equations Try #17 pg.3641 Find all of the solutions of the equation in the interval algebraically.

  8. 5.3 Solving Trigonometric Equations Extracting Square Roots Solve: Add 1 to each side Divide each side by 3 Take the square root of both sides Tan x has a period of so first find all of the solution in the interval [0,). These are and .Add multiples of to get the general form and

  9. 5.3 Solving Trigonometric Equations Try #19 pg.3642 Find all of the solutions of the equation in the interval algebraically.

  10. 5.3 Solving Trigonometric Equations Factoring Solve: Set each factor equal to 0 The equation cot x=0 has the solution in the interval (0, ). No solution is obtained for because are outside the range of the cosine function. Because cot x has a period of the general form of the solution is obtained by adding multiples of to get where n is an integer.

  11. 5.3 Solving Trigonometric Equations Try #21 pg.3643 Find all of the solutions of the equation in the interval algebraically.

  12. Find all solutions of in the interval

  13. Now attempt #28 on p.364

  14. Find all solutions of in the interval

  15. Now attempt #26 on p. 364

  16. Solve

  17. Now attempt #39 on p.365

  18. Solve

  19. Now attempt #45 on p.365

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