Stephanie's Reflection

y=Asin(Bx-h)+C
amplitude is hight
b is period p=2π/b
h is horizontal shift
c is vertical shift

EG: y=2sin(3x+π)-4
up 2, down 2, total height +4
p=2π/3

• 0 +1/6π
• π/6 +1/6
• π/3 +1/6
• π/2 +1/6
• 2π/3

2π/3 / 4= 1/6π
Phase Shift = -π (-1) moving to the left

• 0 -1 = -π
  
• π/6 -1 = -5π/6
  
• π/3 -1 = -2π/3
  
• π/2 -1 = -π/2
  
• 2π/3 -1 = -π/3

Identities:

1. check identities
2. algebra
3. identities

EG: secx-sinxtanx
=1/cosx - sinx/1 (sinx/cos)
=1/cosx - sinx²/cos
=1-sinx²/cosx
sin²+cox²=1
cos²1-sin²
=cos²x/cosx
-cosx

Proving:
EG: cotA(1+tanA)/tanA=csc²A
cotA(sec²A)/tanA
((cosA/sinA)(1/cos²A))/(sin/cos)
(cosA/sinAcosA)/(sinA/cosA)
cos²A/sin²AcosA
=1/sin²A
=csc²A

Factoring:
EG: 2sin²Θ-1=0
2sin²Θ=1
sin²Θ=1/2
sinΘ=+/-√1/2
Θ=sin-¹(+/-√1/2)
Θ=30°, 150°, 210°, 330°
-30+180=150
150+180=210
-210+360=330

Reciprocal Relationships

• cscΘ=1/sinΘ
• secΘ=1/cosΘ
• cotΘ=1/tanΘ

Relationships with Negatives

• sin -Θ= -sinΘ and cos -Θ= -cosΘ
• csc -Θ= -cscΘ and sec -Θ= -secΘ
• tan -Θ= -tanΘ and cot -Θ= -cotΘ

Pythagorean Relationsihps

• sin²Θ+cos²Θ=1
• 1+tan²Θ=sec²Θ
• 1+cot²Θ=csc²Θ

Cofunction Relationships

• sinΘ=cos(90°-Θ) and cosΘ=sin(90°-Θ)
• tanΘ=cot(90°-Θ) and cotΘ=tan(90°-Θ)
• secΘ=csc(90°-Θ) and cscΘ=sec(90°-Θ)