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Angle Sum Formula

How to use formula to express exact values

The angle sum identities take two different formulas
  • sin(A+B) = sinAcosB + cosAsinB
  • cos(A+B) = cosAcosB − sinAsinB
These formulas allow you to express the exact value of trigonometric expressions that you could not otherwise express. Consider the sin(105°). Unlike the sin(30) which can be expressed as ½, the sin(105) cannot simply be represented as a rational expression. However, the angle sum formula allows you to represent the exact value of this function Picture of angle sum formula
USe the angle sum formula to determine the exact value of cos(75°)
Answer
USe the angle sum formula to determine the exact value of sin(75°)
Answer
USe the angle sum formula to determine the exact value of cos(105°)
Answer