Trigonometric Reference Sheet
Pythagorean Identities
sin2x + cos2x = 1
(1)
1 + cot2x = csc2x
(2)
tan2x + 1 = sec2x
(3)
Double Angle Identities
sin(2x) = 2*sin x*cos x
(4)
cos(2x) = cos2x - sin2x
(5)
cos(2x) = 2*cos2x – 1
(6)
cos(2x) = 1 – 2*sin2x
(7)
Half Angle identities
1
cos2x = (1+cos(2x))
2
1
sin2x = (1 – cos(2x))
2
(8)
(9)
Tangent formulas
tan x =
𝑑
𝑑𝑥
sin 𝑥
cos 𝑥
tan x = sec2x
(10)
(11)
Addition and Subtraction formulas
sin(A+B) = sin A*cos B + cos A*sin B
(12)
sin(A – B) = sin A*cos B – cos A*sin B
(13)
cos(A+B) = cos A*cos B – sin A*sin B
(14)
cos(A – B) = cos A*cos B + sin A*sin B
(15)
Product to Sum formulas
1
1
2
2
sin A sin B = cos(A – B) – cos(A + B)
1
1
2
2
cos A cos B = cos(A – B) + cos(A + B)
sin A cos B =
1
2
1
sin(A + B) + sin(A - B)
2
1
1
2
2
cos A sin B = sin(A + B) – sin(A - B)
(16)
(17)
(18)
(19)