Fundamental Trig Identities

Sin^2x

1-cos2x/2

Cos^2x

1+cos2x/2

Tan^2x

1-cos2x/1+cos2x

Csc^2x

2/1-cos2x

Sec^2x

2/1+cos2x

Cot^2x

1+cos2x/1-cos 2x

=2sinxcosx

Double-Angle formula for sine: sin2x

=cos²x - sin²x

=1-2sin²x

=2cos²x - 1

3 Double-Angle formulas for cosine: cox2x

=+/-√1-cosu/2

Half-Angle Formula: sinu/2

=±√1+cosu/2

Half-Angle Formula: cosu/2

=1-cosu/sinu

=sinu/1+cosu

2 Half-Angle Formulas: tanu/2

domain [-1,1] and range [-π/2, π/2], arcsine, arcsin

Define the Inverse Sine Function

it is the function cos⁻¹ with domain [-1,1] and range [0, π]. Also called arccosine(arccos)

Define the Inverse Cosine Function

it is the function tan⁻¹ with domain R and range (-π/2, π/2). Also called arctangent, arctan

Define the Inverse Tangent Function

ksin(x+Φ)

Sums of Sines and Cosines: when Asinx+Bcosx, then _______ by letting k=√A²+B² and cosΦ=A/K, sinΦ=B/K

2tanu/1-tan²u

Double-Angle Formula for tan2u

cos(A-B) =

cosAcosB+sinAsinB

cos(A+B) =

cosAcosB-sinAsinB

sin(A-B) =

sinAcosB-cosAsinB

sin(A+B) =

sinAcosB+cosAsinB

tan(A-B) =

(tanA-tanB)/(1+tanAtanB)

tan(A+B) =

(tanA+tanB)/(1-tanAtanB)

sin(2A) =

2sinAcosA

cos(2A) =

cos^2A-sin^2A

cos(2A) in all cos^2A =

2cos^2A-1

cos(2A) in all sin^2A =

1-2sin^2A

tan(2A)

(2tanA)/(1-tan^2A)

sin^2A in terms of cosA =

(1-cos(2A))/(2)

cos^2A in terms of cosA =

(1+cos(2A))/(2)

sin(A/2)

+- squareroot((1-cosA)/(2))

cos(A/2)

+- squareroot((1+cosA)/(2))

sin²θ+cos²θ

1

1-cos²θ

sin²θ

1-sin²θ

cos²θ

tan²θ+1

sec²θ

tan²θ-sec²θ

-1

sec²θ-1

tan²θ

1+cot²θ

csc²θ

cot²θ-csc²θ

-1

csc²θ-1

cot²θ

Sin (Pi/2 - x)

Cos x

Csc (Pi/2 - x)

Sec x

Sec (Pi/2 - x)

Csc x

Cos (Pi/2 - x)

Sin x

Tan (Pi/2 - x)

Cot x

Cot (Pi/2 - x)

Tan x