10-3

Things you need to know:

• Sin2a = (2sina)(cosa)
• Cos2a = (cos^2a) - (sin^2a)
• Cos2a = 1 - 2sin^2a
• Cos2a = 2cos^2a - 1
• Tan2a = (2tana)/(1 - tan^2a)
• Sina/2 = +/- square root of ((1 - cosa)/2)
• Cosa/2 = +/- square root of ((1 + cosa)/2)
• Tana/2 = +/- square root of ((1 - cosa)/(1 + cosa))
• Tana/2 = +/- (sina/(1 + cosa))
• Tana/2 = +/- ((1 - cosa)/sina)

Example 1: Simplify square root of 1 - cos135/2

• First step is to find out what formula is being used.
• Formula that is being used: Sina/2 = +/- square root of ((1 - cosa)/2).
• Now you use Sina/2 as your formula.
• Plug in 135 into the formula Sina/2.
• Sina/2 = Sin135/2 = Sin67.5
• Final answer: Sin67.5 degrees

Example 2 : Simplify 2sin67.5 degrees(cos67.5 degrees)

• Sin2(67.5 degrees)
• Sin45 degrees
• Final answer: square root of 2/2

Amber :)