# special angles and trig equations and identities

Sin 0 0
Cos 0 1
Tan 0 0
Sin pi/6 1/2
Cos pi/4 Square root of 2/2
Tan pi/6 Square root of 3/3
Cos pi/6 Square root of 3/2
Sin pi/4 Square root of 2/2
Tan pi/4 1
Sin pi/3 Square root of 3/2
Cos pi/3 1/2
Tan pi/3 Square root 3
Sin pi/2 1
Cos pi/2 0
Tan pi/2 Undefined
Sum formula for Sin SinACosB+CosASinB
Sum formula for Cos CosACosB-sinAsinB
Sum formula for Tan tanA+tanB/1-tanAtanB
Difference Formula for sin sin(A-B)= sinAcosB-cosAsinB
Double angle formula for sin sin(2A)= 2sinAcosA
half-angle formula for sin sin(A/2)= (+-)Square root of (1-cosA/2)
tanA sinA/cosA
cotA cosA/sinA
Pythagorean identity 1 sin^2(A) + cos^2(A) = 1
Law of sines a/sinA = b/sinB = c/sinC
Law of cosine a^2 = b^2 + c^2 – 2bc cosA
Parabola: formulas Formulas: y^2 = 4px when parabola on x-axis
x^2 = 4py when parabola on y-axis
Ellipse: formula formula: (x^2/a^2) + (y^2/b^2) = 1
Hyperbola: formulas Formulas: (x^2/a^2) – (y^2/b^2) = 1
double angle formula for cos cos(2A)= cos^2(A)-sin^2(A)
double angle formula for tan tan(2A)= 2tanA/1-tanA
Difference Formulas for cos cos(A-B)= cosAcosB+sinAsinB
Difference Formulas for tan tan(A-B)= tanA-tanB/1+tanAtanB
half-angle formula for cos cos(A/2)= square root of (1+cosA/2)
half-angle formula for tan tan(A/2)= square root of (1-cosA/1+cosA)
Pythagorean identity 2 tan^2(A) + 1 = sec^2(A)
Pythagorean identity 3 1 + cot^2(A)= csc^2(A)
Parabola: Foci for when on x-axis (p,0) for when on y-axis (0,p)
Ellipse: Foci when a is bigger ((+-) square root of (a^2 – b^2), 0)
when b is bigger (0, (+-) square root of (b^2 – a^2))
Hyperbola: Foci When on x-axis, ((+-) square root of (a^2 + b^2), 0)

When on y-axis, (0, (+-)square root of (b^2+a^2))

y = f(x) + c Vertical shift c units up
y = f(x) – c Vertical shift c units down
y = f(x + c) Horizontal shift c units to the left
y = f(x – c) Horizontal shift c units to the right
y = -f(x) Reflection over x-axis
y = f(-x) Reflection over y-axis
y = cf(x) vertical stretch/shrink, when c > 1 it's stretch, (x,y)–> (x,y*c)
y = f(cx) horizontal stretch/shrink, c < 1 it's shrink, (x,y)–> (x*(1/c),y)
a^0 = 1
a^-n = 1/a^n
a^m(a^n) = a^(m+n)
a^m/a^n = a^(m-n)
(a^m)^n = a^m*n
(ab)^n = (a^n)b^n
log base a of 1 = 0
log base a of a = 1
log base a of a^n = n
a^log base a of x = x
log base a of (UV) = log base a of U + log base a of V
log base a of (u/v) = log base a of u – log base a of v
log base a of u^n = n*log base a of U
log base a of U = log base b of U/ log base b of a