Trig 2

Ambiguous Case (SSA)

C2=180-C1 A+C2 <180 then 2 solutions

Inverse function def

One that undies what the original one does

Half Angle Identities

Sin θ/2= sqrroot(1-cosθ/2) Cos θ/2= sqrroot(1+cosθ/2) tan θ/2= sqrroot(1-cosθ/1+cosθ) =sinθ/1+cosθ =1-cosθ/sin

Inverse function ranges

Sin-1= -pi/2 to pi/2 cos-1= 0 to pi tan-1=-pi/2 to pi/2 cot-1= 0 to pi sec-1=0 to pi csc-1= -pi/2 to pi/2

Identity definition

a statement that's true for any replacement of the variable

Law of Cosines (SSS)

a^2=b^3 + c^2-2bc cos A b^22=a^2 + c^2-2ac cos B c^2=a^2 + b^2-2ab cos C

1 sin^2 θ

cos^2 θ

Cofunction Identities

csc(90-θ)= secθ sin(90-θ)= cosθ tan(90-θ)= cotθ

1+cot^2x=

csc^2

Even/Odd Identities

sin(-x) = - sin x cos(-x) = cos x tan (-x) = - tan x csc (-x) = - csc x sec (-x) = sec x cot (-x) = - cot x

Double Angle Identities

sin(2A) = 2sin(A)cos(A) cos(2A) = cos^2 (A)- sin^2 (A) cos(2A)=1-2sin^2A cos(2A)=2cos^2A-1 tan(2A)=2tanA/1-tan^2A

Sum and Difference Identities

sin(α + β) = sin(α)cos(β) + cos(α)sin(β) sin(α - β) = sin(α)cos(β) - cos(α)sin(β) cos(α + β) = cos(α)cos(β) - sin(α)sin(β) cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

Law of Sines

sinA/a=sinB/b=sinC/c

Pythagorean Identities

sin^2x+cos^2x=1 1+tan^2x=sec^2x 1+cot^2x=csc^2x

Power Reducing Identities

sin^2x=(1-cos2x)/2 cos^2x=(1+cos2x)/2 tan^2x=(1-cos2x)/(1+cos2x)

trig(trig^-1 x) =

x