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))) |
|