Math 12x : Precalculus

Cos Double Angle Formula: cos(2θ) = cos²θ-sin²θ
Sin Double Angle Formula: sin(2θ) = 2sinθcosθ
cos2θ-sin2θsin2θcos2θ = cosθ-sinθsinθcosθ cosθ-sinθsinθcosθ = cos²θ-sin²θ-2sinθcosθ2sinθcosθcos²θ-sin²θ
Cos Double Angle Formula: cos(2θ) = 2cos²θ-1
Sin Double Angle Formula: sin(2θ) = 2sinθcosθ
Pythagorean Iden Formula: cos²θ + sin²θ = 1
2cos²θ - 1 = 2(10.1/2)² - 1 = 102.01/2 - 1 = 100.01/2 = cos2θ
2cosθsinθ = 2(10.1/2)(i0.i/2) = 10.1*i0.i/2 = i00.0i/2 = sin2θ
cos²θ+sin²θ = (10.1/2)²+(i0.i/2)² = 102.01/4 + 102.01/4 = 4/4 = 1
Gaussian Elimination
Original
1327
A
512
b
 
 
Row Echelon
1301
EA=U
52
Eb
 
→ y = 2 → x = -1
 
Gauss-Jordan Elimination
Original
1327
A
512
b
 
 
Row Echelon
1301
EA=U
52
Eb
 
 
Reduced Echelon
1001
A⁻¹A=I
-12
A⁻¹b=x
 
→ x = -1, y = 2
 
Original
1327
A
1001
I
 
 
Row Echelon
1301
EA=U
10-21
EI=E
 
 
Reduced Echelon
1001
A⁻¹A=I
7-3-21
A⁻¹I=A⁻¹
 
 
Application
7-3-21
A-1
512
b
 
=
 
-12
x