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Section 14-3: Properties Involving Functions of More Than One Trigonometric Argument

CHAPTER 14: PROPERTIES OF TRIGONOMETRIC AND CIRCULAR Functions. Section 14-3: Properties Involving Functions of More Than One Trigonometric Argument. Objective. Be able to express functions of – x in terms of functions of x .

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Section 14-3: Properties Involving Functions of More Than One Trigonometric Argument

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  1. CHAPTER 14: PROPERTIES OF TRIGONOMETRIC AND CIRCULAR Functions Section 14-3: Properties Involving Functions of More Than One Trigonometric Argument

  2. Objective • Be able to express functions of –x in terms of functions of x. • Be able to express cos (A – B), cos (A + B), sin (A – B), and sin (A + B) in terms of sin A, cosA, sin A, and sin B. • Be able to express tan (A – B) and tan (A + B) in terms of tan A and tan B.

  3. Consider the Functions Find f(-x) and g(-x).

  4. Definition • Even function: • Odd function:

  5. Are the Trig Functions Even or Odd? • Cosine: • Sine: • Tangent: • Secant: • Cosecant: • Cotangent:

  6. Cofunction Properties for Circular Functions

  7. Cofunction Properties for Circular Functions

  8. Composite Argument Properties

  9. Composite Argument Properties

  10. Composite Argument Properties

  11. Examples: • sin 15° • cos 75° • tan 75° • sec 75°

  12. Example • Prove the equation is an identity:

  13. HOMEWORK: PAGE 824 #27-49 ODD

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