1. Algebra Geometry
Arithmetic Triangle Circle
a+b a b a c ad + bc Area = 1 bh Area = πr 2
= + + = 2
c c c b d bd c2 = a 2 + b2 − 2ab cos θ C = 2πr
a
b a d ad
= = a
c b c bc c r
h
d
b
Factoring
x 2 − y 2 = (x − y)(x + y) x 3 − y 3 = (x − y)(x 2 + x y + y 2 ) Sector of a Circle Trapezoid
x 3 + y 3 = (x + y)(x 2 − x y + y 2 ) x 4 − y 4 = (x − y)(x + y)(x 2 + y 2 )
Area = 1 r 2 θ
2 Area = 1 (a + b)h
2
s = rθ
Binomial (for θ in radians only) a
(x + y)2 = x 2 + 2x y + y 2 (x + y)3 = x 3 + 3x 2 y + 3x y 2 + y 3
h
s
Exponents b
xn
xn xm = x n+m = x n−m (x n )m = x nm
xm r
n
1 x xn
x −n = n (x y)n = x n y n = n
x y y Sphere Cone
√
√ √ √ √ x x n
x n/m = m
xn n xy = n
xny n = √ Volume = 4 πr 3 Volume = 1 πr 2 h
y n y
3 3 √
Surface Area = 4πr 2 Surface Area = πr r 2 + h 2
Lines
Slope m of line through (x0 , y0 ) and (x1 , y1 )
r
h
y1 − y0
m=
x1 − x0
r
Through (x0 , y0 ), slope m
y − y0 = m(x − x0 )
Slope m, y-intercept b
Cylinder
y = mx + b Volume = πr 2 h
Surface Area = 2πr h
Quadratic Formula
If ax 2 + bx + c = 0 then
√
−b ± b2 − 4ac h
x=
2a r
Distance
Distance d between (x1 , y1 ) and (x2 , y2 )
d= (x2 − x1 )2 + (y2 − y1 )2
2. Trigonometry
(x, y) sin θ =
y Half-Angle
r
1 − cos 2θ 1 + cos 2θ
r sin2 θ = cos2 θ =
x 2 2
cos θ =
r
y
Addition
tan θ =
x sin(a + b) = sin a cos b + cos a sin b cos(a + b) = cos a cos b − sin a sin b
Subtraction
sin θ =
opp sin(a − b) = sin a cos b − cos a sin b cos(a − b) = cos a cos b + sin a sin b
hyp
hyp adj Sum
opp cos θ =
hyp u+v u−v
sin u + sin v = 2 sin cos
2 2
opp u+v u−v
tan θ = cos u + cos v = 2 cos cos
adj 2 2
adj
Product
sin u sin v = 1 [cos(u − v) − cos(u + v)]
2
Reciprocals cos u cos v = 1 [cos(u − v) + cos(u + v)]
2
1 1 1 sin u cos v = 1 [sin(u + v) + sin(u − v)]
2
cot θ = sec θ = csc θ =
tan θ cos θ sin θ cos u sin v = 1 [sin(u + v) − sin(u − v)]
2
Definitions π/2
2π/3 π/3
cos θ 1 1 π/4
cot θ = sec θ = csc θ = 3π/4
sin θ cos θ sin θ
5π/6 π/6
Pythagorean π 0
sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ Radians
sin(0) = 0 cos(0) = 1
√
π π
Cofunction sin 6 = 1
2 cos 6 = 2
3
√ √
π π
π π π sin = 2
cos = 2
sin 2 − θ = cos θ cos 2 − θ = sin θ tan 2 − θ = cot θ 4 2 4 2
√
π π
sin 3 = 2
3
cos 3 = 1
2
π π
sin =1 cos =0
Even/Odd 2
√
2
sin 2π
3 = 2
3
cos 2π
3 = −1
2
sin(−θ ) = −sin θ cos(−θ) = cos θ tan(−θ) = −tan θ √ √
sin 3π
4 = 2
2
cos 3π
4 =− 2
2
√
sin 5π
6 = 1
2 cos 5π
6 = − 23
Double-Angle sin(π) = 0 cos(π ) = −1
sin 2θ = 2 sin θ cos θ cos 2θ = cos2 θ − sin2 θ cos 2θ = 1 − 2 sin2 θ sin(2π) = 0 cos(2π) = 1
![Trigonometry
(x, y) sin θ =
y Half-Angle
r
1 − cos 2θ 1 + cos 2θ
r sin2 θ = cos2 θ =
x 2 2
cos θ =
r
y
Addition
tan θ =
x sin(a + b) = sin a cos b + cos a sin b cos(a + b) = cos a cos b − sin a sin b
Subtraction
sin θ =
opp sin(a − b) = sin a cos b − cos a sin b cos(a − b) = cos a cos b + sin a sin b
hyp
hyp adj Sum
opp cos θ =
hyp u+v u−v
sin u + sin v = 2 sin cos
2 2
opp u+v u−v
tan θ = cos u + cos v = 2 cos cos
adj 2 2
adj
Product
sin u sin v = 1 [cos(u − v) − cos(u + v)]
2
Reciprocals cos u cos v = 1 [cos(u − v) + cos(u + v)]
2
1 1 1 sin u cos v = 1 [sin(u + v) + sin(u − v)]
2
cot θ = sec θ = csc θ =
tan θ cos θ sin θ cos u sin v = 1 [sin(u + v) − sin(u − v)]
2
Definitions π/2
2π/3 π/3
cos θ 1 1 π/4
cot θ = sec θ = csc θ = 3π/4
sin θ cos θ sin θ
5π/6 π/6
Pythagorean π 0
sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ Radians
sin(0) = 0 cos(0) = 1
√
π π
Cofunction sin 6 = 1
2 cos 6 = 2
3
√ √
π π
π π π sin = 2
cos = 2
sin 2 − θ = cos θ cos 2 − θ = sin θ tan 2 − θ = cot θ 4 2 4 2
√
π π
sin 3 = 2
3
cos 3 = 1
2
π π
sin =1 cos =0
Even/Odd 2
√
2
sin 2π
3 = 2
3
cos 2π
3 = −1
2
sin(−θ ) = −sin θ cos(−θ) = cos θ tan(−θ) = −tan θ √ √
sin 3π
4 = 2
2
cos 3π
4 =− 2
2
√
sin 5π
6 = 1
2 cos 5π
6 = − 23
Double-Angle sin(π) = 0 cos(π ) = −1
sin 2θ = 2 sin θ cos θ cos 2θ = cos2 θ − sin2 θ cos 2θ = 1 − 2 sin2 θ sin(2π) = 0 cos(2π) = 1](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)