cosine, sine, & tangent

y = sin⁻¹ x

domain; range (interval & quadrants)

[-1, 1]; [-^π/₂, ^π/₂]; I & IV

y = cos⁻¹ x

domain; range (interval & quadrants)

[-1, 1]; [0, π]; I & II

y = tan⁻¹ x

domain; range (interval & quadrants)

(-∞, ∞); (-^π/₂, ^π/₂); I & IV

y = cot⁻¹ x

domain; range (interval & quadrants)

(-∞, ∞); (0, π); I & II

y = sec⁻¹ x

domain; range (interval & quadrants)

(-∞, -1] ∪ [1, ∞); [0, -^π/₂) ∪ (^π/₂, π]; I & II

y = csc⁻¹ x

domain; range (interval & quadrants)

(-∞, -1] ∪ [1, ∞); [-^π/₂, 0) ∪ (0, ^π/₂]; I & IV

even function(s)

cosine

odd funtion(s)

tangent & sine

reciprocal identities

cotθ = ¹/_tanθ

secθ = ¹/_cosθ

cscθ = ¹/_sinθ

quotient identites

tanθ = ^sinθ/_cosθ

cotθ = ^cosθ/_sinθ

pythagorean identities

sin²θ + cos²θ = 1

tan²θ + 1 = sec²θ

1 + cot²θ = csc²θ

even odd identities

sin(-θ) = -sinθ

csc(-θ) = -cscθ

cos(-θ) = cosθ

sec(-θ) = secθ

tan(-θ) = -tanθ

cot(-θ) = -cotθ

cosine sum & difference identities

cos(A+B) = cosAcosB - sinAsinB

cos(A-B) = cosAcosB +sinAsinB

cofunction identites

cos(90°-θ) = sinθ

sin(90°-θ) = cosθ

tan(90°-θ) = cotθ

sec(90°-θ) = cscθ

csc(90°-θ) = secθ

cot(90°-θ) = tanθ

sine sum & difference identites

sin(A+B) = sinAcosB + cosAsinB

sin(A-B) = sinAcosB - cosAsinB

tangent sum & difference identites

tan(A+B) = ^{tanA + tanB}/_{1 - tanAtanB}

tan(A-B) = ^{tanA - tanB}/_{1 + tanAtanB}

cosine double-angle indentites

cos 2A = cos²A - sin²A

cos 2A = 1 - 2 sin²A

cos 2A = 2 cos²A - 1

sine double-angle identity

sin 2A = 2 sinAcosA

tangent double-angle indentity

tan 2A = ^{2 tanA}/_{1 - tan²A}

_{cosine half-angle identity}

cos ^A/₂ = ±√^{(1 + cosA)}/₂

sine half-angle identity

sin ^A/₂ = ±√^{(1 - cosA)}/₂

tangent half-angle indetities

tan ^A/₂ = ±√^{(1 - cosA)}/_{1 + cosA}

tan ^A/₂ = ^sinA/_{(1 + cosA)}

tan ^A/₂ = ^{(1 - cosA)}/_sinA

y = arcsin x

y = sin⁻¹ x

y = arccos x

y = cos⁻¹ x

y = arctan x

y = tan⁻¹ x

y = sinx

domain; range; amplitude; period

(-∞, ∞); [-1, 1]; 1; 2π

y = cosx

domain; range; amplitude; period

(-∞, ∞); [-1, 1]; 1; 2π

y = tanx

domain; range; amplitude; period

y = secx

domain; range; amplitude; period

y = cscx

domain; range; amplitude; period

y = cotx

domain; range; amplitude; period