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Chapter 5 Vocabulary

Chapter 5 Vocabulary. Section 5.1 Vocabulary. Reciprocal Identities. Sin(u) = 1/ csc (u) cos (u) = 1/ sec(u) Csc (u) = 1/sin(u) sec(u) = 1/ cos (u) Tan(u) = 1/cot(u) cot(u) = 1/tan(u). Quotient Identities. Tan(u) = sin(u) / cos (u)

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Chapter 5 Vocabulary

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  1. Chapter 5 Vocabulary

  2. Section 5.1 Vocabulary

  3. Reciprocal Identities • Sin(u) = 1/csc(u) cos(u) = 1/ sec(u) • Csc(u) = 1/sin(u) sec(u) = 1/cos(u) • Tan(u) = 1/cot(u) cot(u) = 1/tan(u)

  4. Quotient Identities • Tan(u) = sin(u) / cos(u) • Cot(u) = cos(u) / sin(u)

  5. Pythagorean Identities • Sin2 (u) + cos2 (u) = 1 • 1 + tan2(u) = sec2(u)

  6. Cofunction Identities • Sin(∏/2 – u) = cos(u) • Cos(∏/2 – u) = sin(u) • Tan(∏/2 – u) = cot(u) • Cot(∏/2 – u) = tan(u) • Sec(∏/2 – u) = csc(u) • Csc(∏/2 – u) = sec (u)

  7. Even/ Odd Idetities • Sin(-u) = -sin(u) • Csc(-u) = -csc(u) • Tan(-u) = -tan(u) • Cot(-u) = -cot(u) • Cos(-u) = cos(u) • Sec(-u) = sec(u)

  8. Section 5.2 Vocabulary

  9. Section 5.3 Vocabulary

  10. Section 5.4 Vocabulary

  11. Sum and Difference Formulas • Sin(u + v) = sin(u)cos(v) + cos(u) sin(v) • Sin(u – v) = sin(u)cos(v) – cos(u)sin(v) • Cos(u + v) = cos(u)cos(v) – sin(u) sin(v) • Cos(u – v) = cos(u) cos(v) + sin(u)sin(v) • Tan(u + v) = [tan(u) + tan(v)] / [1- tan(u)tan(v)] • Tan(u – v) = [tan(u) – tan(v)]/[1+tan(u)tan(v)]

  12. Sum and Difference formula Definition • Sum and difference formulas can be used to find exact values of trigonometric functions involving sums or differences of special angles.

  13. Section 5.5 Vocabulary

  14. Double angle Formulas • Sin(2u) = 2sin(u) cos(u) • Cos(2u) = cos2(u) – sin2(u) = 2 cos2(u) -1 = 1 – 2 sin2(u) • Tan(2u) = [2tan(u)]/[1-tan2(u)]

  15. Power reducing Formulas • sin2(u) = [1-cos(2u)]/2 • cos2(u) = [1+cos(2u)]/2 • Tan2(u) = [1-cos(2u)]/[1+cos(2u)]

  16. Half-Angle Formulas • Sin(u/2) = +/- √ [ (1-cos(u))/2] • Cos(u/2) =+/- √ [(1+cos(u))/2] • Tan(u/2) = (1-cos(u))/sin(u) = sin(u) / (1+cos(u))

  17. Product-to-sum Formulas • Sin(u)sin(v) = ½ [cos(u-v)-cos(u+v)] • Cos(u)cos(v) = ½ [cos(u-v)+cos(u+v)] • Sin(u) cos(v) = ½ [sin(u+v) + sin(u-v)] • Cos(u)sin(v) = ½ [sin(u+v)-sin(u-v)]

  18. Sum to Product formulas • Sin(u) + sin(v) = 2 sin((u+v)/2) cos((u-v)/2) • Sin(u) - sin(v) = 2cos((u+v)/2) sin((u-v)/2) • Cos(u) + cos(v) = 2cos((u+v)/2) cos((u-v)/2) • Cos(u) – cos(v) = -2sin((u+v)/2) sin((u-v)/2)

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