1. Ch 5.5

2. HW questions?

3. 4 more categories of trig identities
Multiple angles
EX: sin(ku) cos(ku)
Squares of trig functions
EX: 𝑠𝑖𝑛 2 𝑥 𝑐𝑜𝑠 2 𝑥
Half angles
EX: sin( 𝑥 2 ) cos( 𝑥 2 )
Products of trig functions
EX: cos(u)sin(v)

4. EX 1: Evaluating functions involving double angles
Given cos(Ɵ) = 5 13
and 3П 2 < Ɵ < 2П
Find
sin(2 Ɵ) 2) Cos(2 Ɵ ) 3)Tan(2 Ɵ )

5. EX 2:Solving a Multiple-Angle Equation
Solve 2 cos(x) + sin(2x) = aka what angles make this equation true?
2cos(x) + 2sin(x)cos(x) = 0 Use Double-Angle formula
2cos(x)[1+ sin(x)] = 0 Factor
2cos(x) = and sin(x) = 0 Set each to 0 and solve
cos(x) = 0 sin(x) = -1
x = П 2 and 3П 2 and x = 3П on the interval [0, 2П)
General solution: x = П 2 + Пn

6. EX 3: Simplify y = 4 cos²(x) – 2 using the double angle formulas
EX 3: Simplify y = 4 cos²(x) – 2 using the double angle formulas. Then graph.

8. EX 5: Using the Half Angle Formulas to find exact values of trig functions
Find the exact value of sin(105ᴼ) Notice that 105ᴼ is half of 210ᴼ, which is one of our special angles. Sin is positive in quadrant II so we have: Sin(105ᴼ) = 1 −cos⁡(210ᴼ) 2 = 1 −(− 3 /2) 2 =
If an angle is half of one of our “special angles,” we can use the half angle formulas to find exact values.