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Basic Trigonometric Identities

Learn how to recall basic trigonometric identities, Pythagorean identities, and proven strategies to solve identities. Explore steps to separate, simplify, and prove trig identities effectively. Includes worked examples and homework exercises for practice.

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Basic Trigonometric Identities

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  1. Basic Trigonometric Identities Section 15.1

  2. Recall Basic Trig Identities

  3. Pythagorean Identities

  4. Strategy for Proving Identities • Separate the equation into a left-side expression and right-side expression and work with these separately. • Simplify the more complicated side, looking for ways to use the basic trig identities • After simplifying one side as much as you can, try working with the other side until both sides are the same. • Worst case scenario: express both sides in terms of sine and cosine. Then, clean up your mess. 

  5. EXAMPLE: (note restrictions) • Prove

  6. EXAMPLE: (note Restrictions) • Prove

  7. EXAMPLE: (note Restrictions) • Prove

  8. EXAMPLE: (Note Restrictions) • Prove:

  9. Homework: • p. 663-665, #9-27(odd)

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