Terms, Concepts and Things to Remember

Mathematics 114 with Camacho at University of Wisconsin - Madison

About this deck

By: Melanie Shibley
Textbook:

Precalculus: A Prelude to Calculus
Created: 2010-10-21
Size: 65 flashcards
Views: 61

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when you're given the slope of a line and one point, what formula do you use?

Point-Slope Form: y-y1=m(x-x1)

When you're given only two points , find the equation of the line by:

1.) first, finding m: y2-y1/x2-x1
2.) then, plug m in to the point-slope form equation and use either set of points.

if two lines are perpendicular, their slopes will be:

Reciprocal and opposite (if one is +, the other will be -)

to find a common intersection between three lines, you must:

1.) set two of them equal to each other and solve for x
2.) plug x and either m value into the equation to get y
3.) plug x and y back into the equation with no numerical values and solve for m

given g(x) = f(x+b) +c. where in this function can you find the shifts?

f= stretched or shrunk by this value
(x+b) = shifted to the left or right by this value
c= shifted up or down by this value
- or + (f) = denotes the direction the parabola will open

how do you find the vertex from an equation in the form (x+t)² + c

t(f(t)) is the vertex.
or, (t,c)

how do you find the degree of a polynomial?

find the highest power in the polynomial; this is the degree

for |x| very large, the numerator and denominator (largest terms excluded):

are approximately 1

what is a rational function?

a function of the form r(x) = p(x) / q(x) where p and q are polynomials, and q can't equal 0.

How do you divide polynomials?

use standard long division

define a sum and difference of two complex numbers

(a+bi) + (c+di) = (a+c) +(b+d)i

(a+bi)-(c+di) = (a-c) + (b-d) i

What is the complex conjugate?

if the expression is (a + bi), its complex conjugate is (a-bi)

Define multiplication of complex numbers

(a+bi)(c+di) = (ac-bd) + (ad-bc)i

Define division of complex numbers

(a+bi) / (c+di) = (ac + bd/c²+d²) + (bc-ad/c²+d²) i

What are the three ways to solve systems of linear equations?

substitution, standard elimination, and gaussian elimination with matrices

log_by=

logy/logb

log_b(xy)=

log_bx+log_by

log_b(x/y) =

log_bx-log_by

log_by^t =

tlog_by

Describe the expression B(t) = Pe^rt

B(t) = final amount

P= initial amount

r = growth/decay rate

t =time

Area of a trapezoid

1/2 (b1+b2)h

Area of an ellipse/ equation in ellipse form

area = πab when the equation is in x²/a²+y²/b²=1 form

Area Stretch Theorem

The area of R' = cd times the original area (R)

what is the definition of e?

e is the number such that area(1/x,1,e) =1

lnx is a shorthand way of writing what?

log_ex

What is the equation for the doubling time of a system?

70/R, where r = growth rate

What is the equation for the doubling rate of a system?

70/t, where t=time in years

how do you find the center, r, and area of a circle given in x²+hx+y²+ky=c form?

you complete the square, yielding the form (x-h)²+(y-k)²=r². from here you can find the center (h,k) and radius (r). area = πr²

any point in the region from π/2-->π is...

negative

what is the equation to find arc length?

L=øπ/180

what is the equation to find the area of a slice?

s=1/2ør²

How do you convert from degrees to radians?

øπ/180

how do you convert from radians to degrees?

180/π

how do you find the 4 smallest + numbers ø such that sin or cosø = 0,-1 or 1?

go around the unit circle counterclockwise, stopping each time sin or cos= given integer x. do this 4 times. find the 1st one, add 2π to it to get the next one, etc...

how do you find the 4 smallest + numbers ø such that sin or cosø = 1/2 or √3/2?

find the first ø. (ex 30º). find the next ø in line on the unit circle (ex 150º). these are your 1st two numbers. Then, add your original ø to 360º, which yields the 3rd number. finally, add your second ø to 360 to get the 4th number.

secantø=

1/cosø

cosecantø=

1/sinø

cotangentø=

cosø/sinø

what is another way to write cotangent?

1/tanø

write tanø in terms of cosø

tanø= √(1-cos²ø)/cosø

write secant in terms of tanø

1+tan²ø=sec²ø

what are the 3 trig identities with (π/2-ø)?

cos(π/2-ø) = sinø

sin(π/2-ø) = cosø

tan(π/2-ø) = 1/tanø

What are the 3 trig identities with (90-ø)?

cos(90-ø)= sinø

sin(90-ø)= cosø

tan(90-ø)= 1/tanø

What are the 3 trig identities with (ø+π)?

cos(ø+π) = -cosø

sin(ø+π) = -sinø

tan(ø+π) = tan ø

what are the 3 trig identities with (ø+2π)?

cos(ø+2π) = cosø

sin(ø+2π) = sinø

tan(ø+2π) = tanø

About this deck

By: Melanie Shibley
Textbook:

Precalculus: A Prelude to Calculus
Created: 2010-10-21
Size: 65 flashcards
Views: 61

About StudyBlue

“I have been getting MUCH better grades on all my tests for school. Flash cards, notes, and quizzes are great on here. Thanks!”
Kathy