Unit 2.2: Compound Angles and Double angles

  • Certain angle pairs are given special names based on their relative position to one another or based on the sum of their respective measures.
  • If two angles are subtracted then they are called Compound angles.
  • (A-B) are compound angles because two angles are subtracted.
  • cos(A-B) = cosAcoB + sinAsinB RHS expanded
  • It should be known both ways.
  1. cosA – B = cosAcosB + sinAsinB
  2. cosA + B =cosAcosB – sinAsinB
  3. sinA – B = sinAcosB – cosAsinB
  4. sinA + B = sinAcosB + cosAsinB
  • These are the 4 compound identities that will be studied
  • all the angles in orange are compounded angles.
  • On the RHS are the expanded compound angles
  • It should be known in both ways (LHS and RHS)

Why Compound angles?

  • e.g. sin75º determine the value of sin75º without using a calculator
  • 75º is not a special angle so we have a PROBLEM .
  • For a calculator not to be used  we will need special angles .
  • 75* is an angle between 0* and 90* so special angles can be used.



instructions



Double angles



What is the need of double angles? Lets look at an example where the double angles come into play.

Example

Simplify to a single tig ratio without the use of a calculator.