Chapter 4

Chapter 4

1. Even & Odd identities

   • Odd function: where f(-x) = -f(x)
     • Even function: where f(-x) = f(x)
       • Cosine and Secant are even identities, where Cos(-x) =Cos(x) and Sec(-x) = Sec(x)
       • Even can be mirrored across the y-axis or x=0.
     • Sine, Tan, Cot, & Csc are all odd functions. Sin(-x) = -sin(x), Tan(-x) = -Tan(x), Cot(-x) = -cot(x), & csc(-x) = -csc(x)
     • Odd can rotate 180° around the origin

2. Sum/Difference identities

   • sin(x+/- y) = sin(x)*cos(y) +/- cos(x)*sin(y)
     • cos(x-/+ y) = cos(x)*cos(y) -/+ sin(x)*sin(y)
       • Sine always uses the same sign that its angles do. Addition-Addition, Subtraction-subtraction. Cosine always uses the opposite sign that the angles inside its parenthesis do. Addition-Subtraction, Subtraction-Addition.
         • If it is said "Cosine is 4/5", that doesn't mean Cosine(4/5), it means Cosine(x)=4/5. this applies to the other functions as well.

3. Double angles

   • Sin(2x) = 2sinxcosx
     • Cos(2x) = (cos^2)*x- (sin^2)*x = 2(cos^2)*x-1 = 1- 2*(sin^2)*x

4. Half-Angle identities

   • sin(x/2) = +/- the square root of ((1 - cos x ) / 2)
     • Cos(x/2)= +/- the square root of ((1+ cos(2x))/2)