Math 118 Exam 3 Study Guide

Steps for a sequence of transformation

Steps for a sequence of transformation

1. Horizontal shift/compression

2. Horiztonal stretch

3. Vertical reflection

4. Vertical shift/compression

5. Horizontal reflection

6. Vertical shift

Define the variables for y=a(bˣ)+c

A is the initial amount (amount at zero), b is the growth factor, x is the number of growth periods and c is the horizontal asymptote

Describe b=1+r

The growth factor equals the growth rate plus one

Rewrite y=bˣ

x=logᵦy

bʳ * bˢ = ____?

bʳ+ˢ

logᵦ(rs) = ____?

logᵦr + logᵦs

bʳ/bˢ = ____?

bʳ-ˢ

logᵦ(r/s) = ____?

logᵦr - logᵦs

(bʳ)ˢ = ____?

bʳ*ˢ

logᵦ(rˢ) = ____?

s*logᵦ(r)

Rewrite a=bᶜ

logᵦ(a)=c

aˡᵒᵍa⁽ⁿ⁾=____?

n

logₐa⁽ⁿ⁾=____?

n

logₐ(x*y)=____?

logₐ(x)+logₐ(y)

logₐ(x/y)=____?

logₐ(x)-logₐ(y)

logₐ(xʸ)=____?

y*logₐ(x)

Exponentiate m = n

a^m=a^n

Take the log of m = n

logsubam = logsuban

Change of base formula?

Y=b^x, x = logsubay/logsubb

Amplitude formula

maximum value - minimum value / 2

cos(x) = ___?

sin(x + pi/2)

secant =

1/cosx

cosecant =

1/sinx

tangent =

sinx/cosx

cotangent =

cosx/sinx

What is k notation?

x = pik, where k is an integer

What is the period for sin?

2pi

What is the period for cos?

2pi

What is the amplitude definition?

The distance from the middle to the max OR min

What is the amplitude of sin?

1

What is the amplitude of cos?

1

Equilibrium value definition:

The middle value

What is the equilibrium value of all BASE functions?

0

What is the asymptote of cosecant?

vertical at intervals of pi

What is the period of cosecant?

2pi

What is the period of secant?

2pi

What is the period of tangent?

pi

What is the period of cotangent?

pi

formula for sine

y=Asin(B(x+c)) + D

What is a

amplitude

what is b?

horizontal shift/compression

what is c?

horizontal shift

What is d?

equilibrium value

What does the period equal?

2pi/b

Graph the unit circle

okay :)

cost = ?

x coordinate

sint = ?

y coordinate

cos^2t+sin^2t=1

true

What is the circumference of the unit circle?

2pi

What direction are you going if t > 0?

counter-clockwise

What direction are you going if t < 0?

clockwise

sin (pi - t) = ?

sint

cos (2pi - t) = ?

cost and cos-t

sin (pi + t) = ?

-sint

cos (pi + t) = ?

-cost

Draw a 30-60-90 triangle

okay :)

Draw a 45-45-90 triangle

okay :)

sin theta =

opp/hyp

cos theta =

adj/hyp

tan theta +

opp/adj

arc length = ?

radians x radius

d/360 = ?

r/2pi

How do you get from radians to degrees?

multiply by 180/pi

How do you get from degrees to radians?

multiply by pi/180

?^2 + ?^2= ?^2

x, y, r

Coordinates on a non-unit circle?

(rcostheta, rsintheta)

REMEMBER

whether you should be in radians or degrees