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The University of Winnipeg

  

DEPARTMENT OF
MATHEMATICS & STATISTICS

Precalculus Review Workshop




Pythagorean Identities

Provided that all trigonometric functions below are defined for x, the three pythagorean identities are:
  1. sin2(x)+cos2(x)=1
  2. tan2(x)+1=sec2(x)
  3. 1+cot2(x)=csc2(x).
Pythagorean identities.

Sum and Difference Formulas

Recall the sum and difference formulas for sine and cosine:
  1. sin(x+y)=sin(x)cos(y)+cos(x)sin(y)
  2. sin(xy)=sin(x)cos(y)cos(x)sin(y)
  3. cos(x+y)=cos(x)cos(y)sin(x)sin(y)
  4. cos(xy)=cos(x)cos(y)+sin(x)sin(y).
Sum and difference formulas.

Double Angle Identities

If we substitute y=x into the addition formulas above, we obtain the double angle formulas for sine and cosine. These formulas are very important in calculus.
  1. sin(2x)=2sin(x)cos(x)
  2. cos(2x)=cos2(x)sin2(x)=12sin2(x)=2cos2(x)1
  3. cos2x=1+cos(2x)2
  4. sin2x=1cos(2x)2
Double angle formulas example 1
Double angle formulas example 2

Problem Set 5.4

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