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Precalculus Practice: Solving Trigonometric Identities and Equations

This document outlines essential practices for Precalculus students, focusing on solving trigonometric equations and identities. It includes a review session of previous quizzes, detailed examples of calculating exact trigonometric values using given information, and student practice sessions to solidify understanding. With the midterm exams approaching, students are encouraged to engage deeply with trigonometric identities and their applications. This review will help prepare for the critical exam, which constitutes 25% of their overall grade.

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Precalculus Practice: Solving Trigonometric Identities and Equations

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  1. 25 March 2011 Precalculus

  2. Solve 4(3x – 1) +2x = 24 for x. • x = • x = • x = 8 • x = 3 • x = 2 300 0 of 30

  3. COMING MONDAY…… • MIDTERM EXAMS!!!!!!!!!!!!!!! • This exam counts as 25% of your grade, so answering C for all questions will NOT be a good idea

  4. Agenda • Go over quiz – answer any questions • Calculate an exact trigonometric value based on given information. • Student Practice (30 min) • Simplifying Trigonometric Expression • Student Practice (15 min)

  5. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. • Using Trig Identities

  6. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x • Using Trig Identities

  7. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = • Using Trig Identities

  8. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = • Using Trig Identities

  9. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = = • Using Trig Identities

  10. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = = Do: 1 / (3 / 2) = • Using Trig Identities

  11. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = = Do: 1 / (3 / 2) = 0.666… • Using Trig Identities

  12. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = = Do: 1 / (3 / 2) = 0.666… Math  Enter  Enter • Using Trig Identities

  13. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If sec x = , find cos x sec x = = Do: 1 / (3 / 2) = 0.666… Math  Enter  Enter = • Using Trig Identities

  14. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q • Using Trig Identities

  15. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q • Using Trig Identities

  16. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q ( )2 = 1 + cot2q • Using Trig Identities

  17. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q ( )2 = 1 + cot2q ( ) = 1 + cot2q • Using Trig Identities

  18. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q ( )2 = 1 + cot2q ( ) = 1 + cot2q ( ) = cot2q • Using Trig Identities

  19. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q ( )2 = 1 + cot2q ( ) = 1 + cot2q ( ) = cot2q = cot q • Using Trig Identities

  20. Trigonometric Identities 3/22 Use the given information to find the trigonometric value. Example: If cscq = , find tan q csc2q = 1 + cot2q ( )2 = 1 + cot2q ( ) = 1 + cot2q ( ) = cot2q = cot q = tan q • Using Trig Identities

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