| Formula | Identity | Formula | Identity |
|---|---|---|---|
| sin(π/2–A) | cos A | cos(π/2–A) | sinA |
| sin(π/2+A) | cos A | cos(π/2+A) | –sinA |
| sin(3π/2–A) | – cos A | cos(3π/2–A) | –sinA |
| sin(3π/2+A) | – cos A | cos(3π/2+A) | sinA |
| sin(π–A) | sin A | cos(π–A) | –cosA |
| sin(π+A) | – sin A | cos(π+A) | –cosA |
| sin(2π–A) | – sin A | cos(2π–A) | cosA |
| sin(2π+A) | sin A | cos(2π+A) | cosA |
All trigonometric identities are cyclic in nature. They repeat themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is true for cos 45° and cos 225°. Refer to the above trigonometry table to verify the values.
| Formula | Identity |
|---|---|
| sin(x+y) | sin(x)cos(y)+cos(x)sin(y) |
| cos(x+y) | cos(x)cos(y)–sin(x)sin(y) |
| tan(x+y) | (tanx+tany)/(1−tanx•tany) |
| sin(x–y) | sin(x)cos(y)–cos(x)sin(y) |
| cos(x–y) | cos(x)cos(y)+sin(x)sin(y) |
| tan(x−y) | (tanx–tany)/(1+tanx•tany) |
| cos(2π–A) | cosA |
| cos(2π+A) | cosA |
| Formula | Identity | Identity 2 |
|---|---|---|
| sin(2x) | [2tanx/(1+tan2x)] | 2sin(x)•cos(x) |
| cos(2x) | [(1-tan2x)/(1+tan2x)] | cos2(x)–sin2(x) |
| cos(2x) | 1–2sin2(x) | 2cos2(x)−1 |
| tan(2x) | [2tan(x)]/[1−tan2(x)] | |
| sec(2x) | sec2x/(2-sec2x) | |
| csc(2x) | (secx.cscx)/2 | |
| Sin3x | 3sin x – 4sin3x | |
| Cos3x | 4cos3x-3cos x | |
| Tan3x | [3tanx-tan3x]/[1-3tan2x] | |
| sin(x/2) | ±√((1−cosx)/2) | |
| cos(x/2) | ±√((1+cosx)/2) | |
| tan(x/2) | √((1−cos(x))/(1+cos(x))) |