| tan(θ) | sin(θ)/cos(θ) |
| cot(θ) | cos(θ)/sin(θ) |
| sin2(θ) + cos2(θ) | 1 |
| sec2(θ) - tan2(θ) | 1 |
| csc2(θ) - cot2(θ) | 1 |
| sin(π/2 - θ) | cos(θ) |
| cos(π/2 - θ) | sin(θ) |
| tan(π/2 - θ) | cot(θ) |
| cot(π/2 - θ) | tan(θ) |
| csc(π/2 - θ) | sec(θ) |
| sec(π/2 - θ) | csc(θ) |
| sin(2θ) | 2sin(θ)cos(θ) |
| cos(2θ) | cos2(θ) - sin2(θ) |
| cos(2θ) | 2cos2(θ) - 1 |
| cos(2θ) | 1 - 2sin2(θ) |
| tan(2θ) | 2tan(θ)/[1 - tan2(θ)] |
| sin(θ) + sin(ϕ) | 2sin((θ + ϕ)/2)cos( (θ - ϕ)/2) |
| sin(θ) - sin(ϕ) | 2cos((θ + ϕ)/2)sin( (θ - ϕ)/2) |
| cos(θ) + cos(ϕ) | 2cos((θ + ϕ)/2)cos( (θ - ϕ)/2) |
| cos(θ) - cos(ϕ) | -2sin((θ + ϕ)/2)sin( (θ - ϕ)/2) |
| sin(θ) | 1/csc(θ) |
| cos(θ) | 1/sec(θ) |
| tan(θ) | 1/cot(θ) |
| csc(θ) | 1/sin(θ) |
| sec(θ) | 1/cos(θ) |
| cot(θ) | 1/tan(θ) |
| sin(-θ) | -sin(θ) |
| cos(-θ) | cos(θ) |
| tan(-θ) | -tan(θ) |
| csc(-θ) | -csc(θ) |
| sec(-θ) | sec(θ) |
| cot(-θ) | -cot(θ) |
| sin(θ ± ϕ) | sin(θ)cos(ϕ) ± cos(θ)sin(ϕ) |
| cos(θ ± ϕ) | cos(θ)cos(ϕ) ∓ sin(θ)sin(ϕ) |
| tan(θ ± ϕ) | [tan(θ) ± tan(ϕ)]/[1 ∓ tan(θ)tan(ϕ)] |
| sin2(θ) | [1 - cos(2θ)]/2 |
| cos2(θ) | [1 + cos(2θ)]/2 |
| tan2(θ) | [1 - cos(2θ)]/[1 + cos(2θ)] |
| sin(θ)sin(ϕ) | [cos(θ - ϕ) - cos(θ + ϕ)]/ 2 |
| cos(θ)cos(ϕ) | [cos(θ - ϕ) + cos(θ + ϕ)]/ 2 |
| sin(θ)cos(ϕ) | [sin(θ + ϕ) + sin(θ - ϕ)]/ 2 |
| cos(θ)sin(ϕ) | [sin(θ + ϕ) - sin(θ - ϕ)]/ 2 |