77 terms

Sin2x

2(sinx)(cosx)

1.) Cos2x

Cos^2x-Sin^2x

2.) Cos2x

2cos^2x-1

3.) Cos2x

1-2sin^2x

Sec^2x

1+tan^2x

log(baseb)b

1

x^(-a)

1/(x^a)

x^a * x^b

X^ (a+b)

x^a /x^b

x^ (a-b)

(x^a)^b

x^ab

x^0

1

x^a * y^a

(xy)^a

log(baseb)(p*g)

log(baseb)p + log(baseb)g

log(baseb)(p/g)

log(baseb)p- log(baseb)g

is r a zero of a polynomial?

r is a zero of the polynomial p(x) if and only if x-r is a divisior of p(x)

What is the remainer of P(x) divided by (x-r)?

If polynomial p(x) is divided by x-r then the remainder is p(r)

What are the rational zeros of p(x)?

divisors or constant term/divisors of leading coefficient

What is another zero of an equation with zero 3+2i

3-2i

number of positive real zeros of polynomial p(x)

equal to number of sign changes between terms or less than that number by an even integer

domain

x values

range

y values

function

each x value only has one y

relation

set of ordered pairs

(f+g)(x)

f(x)+g(x)

(f-g)(x)

f(x)-g(x)

(fg)(x)

f(x)*g(x)

(f/g)(x)

f(x)/g(x)

(fog)(x)

f(g(x))

f^-1

inverse

f(x)*f(x)^-1

x

inverse has to be a function?

false

graph of inverse

reflected across line y=x

even function

f(-x)=f(x) x,y -x,y symmetric across y axis

odd function

f(-x)=-f(x), x,y -x,-y, symmetric with respect to the origin

sum of even functions

even

sum of odd functions

odd

product of even and odd function

odd

general equation of linear functions

ax+by+c=0

slope of linear with general equation

-a/b

y intercept with general equation

-c/b

general form of quadratic

ax^2+bx+c=y

for quad, a>0

opens up

for quad, a<0

opens down

x-coordinate of vertex of parabola

-b/2a

axis of symmetry of parabola

x=-b/2a

vertex of parabola

-b/2a, c-(b^2/2a)

even funtion ends

same direction

odd function ends

opp direction

45-45-90 triangle

1,1, square root of 2

30-60-90 triangle

1, square root of 3, 2

general form of trigonometric function

y=a*f(bx+c)

general form of trig, a is

amplitude

general form of trig, b is

normal per of f/b =period

phase shift, general form of trig

-c/b

periods of sin, cos tan

sin an dcos 2pi, tan is pi

1+cotx^2

cscx^2

1+tanx^2

secx^2

sinx^2+cosx^2

1

cos(90-x)

sinx

sin(pi/2-x)

cosx

csc(90-x)

secx

sec(pi/2-x)

cscx

cot(90-x)

tanx

tan(pi/2-x)

cotx

area of tri

.5bcsina

b^(log base b of p)

p

translate 4 units to right

f(x-4)

translate 4 units up

f(x)+4

parabola with x orientation

(y-k)^2=4p(x-h) p>0 opens rt.

parabola with y orientation

(x-h)^2=4p(y-k) p>0 opens up

conics p

distance from parabola to the focus and directrix

ellipse x orientation

(x-h)^2/a^2+(y-k)^2/b^2=1

ellipse major/minor axis

2a, 2b

ellipse distance to focus

c=square root of (a^2-b^2)

hyperbola with x orientation, opens to sides

(x-h)/a^2-(y-k)^2/b^2=1

hyperbola with x orientation, asymptote

y-k=+-(b/a)(x-h)

hyperbola distance to focus

c=square root of a^+b^2