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Comprehensive Trigonometric Equations Solver Guide

Learn how to find all solutions for trigonometric equations in radians and degrees within specified intervals. Includes step-by-step examples and explanations using Factor, Zero Product Property, and more.

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Comprehensive Trigonometric Equations Solver Guide

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  1. 14.7 Solving Trig Equations

  2. Find all solutions of for the interval0 <   360. Original equation Solve for 0. Distributive Property Simplify. Divide each side by –1. Factor. Example 7-1a Example:

  3. or Example 7-1a Now use the Zero Product Property. Answer: The solutions are 30°, 150°, and 270°.

  4. Find all solutions of for the interval 0 <   2. Original equation Solve for 0. Factor Example 7-1a Example:

  5. or Answer: The solutions are Example 7-1a Use the Zero Product Property.

  6. Find all solutions of each equation for the given interval. a. b. Answer: Example 7-1b More problems: Answer: 

  7. Solve for all values of ifis measured in radians. Original equation Subtract Factor. or Zero Product Property Solve. Example 7-2a Example:

  8. Look at the graph of to find solutions of The solutions are and so on, and so on. Example 7-2a

  9. The only solution in the interval 0 to are andThe period of the sine function is radians. So thesolutions can be written as andwhere k is any integer. Similarly, the solutions for Example 7-2a

  10. Answer: The solutions are and Example 7-2a

  11. Solve for all values of if ismeasured in degrees. Original equation Solve for 0. Factor. Example 7-2a Example:

  12. Solve for in the interval of or Answer: The solutions are Example 7-2a

  13. a. Solve for all values of if is measured in radians. b. Solve for all values of if is measured in degrees. Answer: Answer: Example 7-2b There is more:

  14. Solve Original equation Multiply. Factor. Example 7-3a Example:

  15. or Example 7-3a

  16. is undefined. Thus, is not a solution. Answer: The solution is Example 7-3a Check

  17. Solve Answer: The solution is . Example 7-3b Your turn:

  18. Solve Original equation Subtract 1 and add to each side. Multiply each side by 4. Factor. Example 7-4a Example:

  19. or is undefined for Answer: The solutions are and Example 7-4a

  20. Solve Answer: Example 7-4b Your turn again:

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