Formulae
Formulae
Formulae
an = , + n, n Z
cos 2
cos
cot = , + n, n Z
sin
tan cot = 1
1
sec = , + n, n Z
cos 2
1
cosec = , + n, n Z
sin
Pythagorean identity
sin2 + cos2 = 1
1
1 + tan2 =
cos2
1
1 + cot2 =
sin2
Sum-Difference Formulas
Power-reduction formula
1 - cos 2
sin2 =
2
1 + cos 2
cos2 =
2
3 sin - sin 3
sin3 =
4
3 cos + cos 3
cos3 =
4
+ -
sin + sin = 2 sin cos
2 2
- +
sin - sin = 2 sin cos
2 2
+ -
cos + cos = 2 cos cos
2 2
+ -
cos - cos = -2 sin sin
2 2
sin( + )
tan + sin =
cos cos
sin( - )
tan - sin =
cos cos
sin( + )
cot + sin =
sin sin
sin( - )
cot - sin =
sin sin
a sin + b cos = r sin ( + ),
b b
where r2 = a2 + b2, sin = , tan =
r a
1
sin sin = (cos( - ) - cos( + ))
2
1
sin cos = (sin( + ) + sin( - ))
2
1
cos cos = (cos( + ) + cos( - ))
2
2 tan (/2)
sin =
1 + tan2 (/2)
1 - tan2 (/2)
cos =
1 + tan2 (/2)
2 tan (/2)
tan =
1 - tan2 (/2)
1 - tan2 (/2)
cot =
2 tan (/2)