Chapter 5 Analytic Trig Formulas

cotangent-cosecant Pythagorean

1+cot²(Θ)=csc²(Θ)

tangent-secant Pythagorean

1+tan²(Θ)=sec²(Θ)

Heron's Triangle Formula

AreaΔ=√k(k-a)(k-b)(k-c), where k is the perimeter of triangle, and a,b,c are all of the sides

Area of a Triangle

K=1/2ab sin(C)

cosine negative

cos(-x)=cos(x)

Double Angle Cosine

cos(2α)=2cos²(α)-1

Cosine Half-Angle

cos(x/2)=±√1+cos(x)/2

Cofunction of cosine

cos(y)=sin(π/2-y)

Addition Cosine

cos(α±β)=cos(α)cos(β) (upside↓±) sin(α)sin(β)

cotangent negative

cot(-x)=-cot(x)

Cofunction of cotangent

cot(y=)tan(π/2-y)

Cotangent definition

cot(Θ)=1/tan(Θ)

cosecant negative

csc(-x)=-csc(x)

Cofunction of cosecant

csc(y)=sec(π/2-y)

Cosecant definition

csc(Θ)= 1/sin(Θ)

Law of Cosines

c²=a²+b²-2abcos© or cos©=a²+b²-c²/2ab

secant negative

sec(-x)=sec(x)

Cofunction of secant

sec(y)=csc(π/2-y)

Secant definition

sec(Θ)=1/cos(Θ)

sine negative

sin(-x)=-sin(x)

Double Angle Sine

sin(2α)=2sin(α)cos(α)

Law of Sines

sin(A)/a=sin(B)/b=sin(C)/c

Sine Half-Angle

sin(x/2)=±√1-cos(x)/2

Cofunction of sine

sin(y)=cos(π/2-y)

Addition Sine

sin(α±β)=sin(α)cos(β)±sin(β)cos(α)

sine-cosine Pythagorean

sin²(Θ)+cos²(Θ)=1

tangent negative

tan(-x)=-tan(x)

Double Angle Tangent

tan(2α)=2tan(α)/1-tan²(α)

Tangent Half-Angle

tan(x/2)=sin(x)/1+cos(x)=1-cos(x)/sin(x)

Cofunction of tangent

tan(y)=cot(π/2-y)

Addition Tangent

tan(α±β)=tan(α)±tan(β)/1(upside↓±)tan(α)tan(β)