Equations

Question 1

What is an even function?

Answer 1

It is a function that is symmetric about the y axis

Question 2

What is an odd function?

Answer 2

It is a function that is symmetric about the origin

Question 3

What is the equation for continuous compounding?

Answer 3

A=P(e^rt)

Question 4

What are the pythagorean identities?

Answer 4

sin^2(θ)+cos^2(θ)=1
tan^2(θ)+1=sec^2(θ)
1+cot^2(θ)=csc^2(θ)

Question 5

What are the even and odd identities?

Answer 5

sin(-x)=-sin(x)
cos(-x)=cos(x)
tan(-x)=-tan(x)

Question 6

What are the product to sum formulas?

Answer 6

sin(x)sin(y)=1/2[cos(x-y)-cos(x+y)]
cos(x)cos(y)=1/2[cos(x-y)+cos(x+y)]
sin(x)cos(y)=1/2[sin(x+y)+sin(x-y)]
cos(x)sin(y)=1/2[sin(x+y)-sin(x-y)]

Question 7

What are the sum to product formulas?

Answer 7

sin(x)±sin(y)=2sin((x±y)/2)cos((x∓y)/2)
cos(x)+cos(y)=2cos((x+y)/2)cos((x-y)/2)
cos(x)-cos(y)=-2sin((x+y)/2)sin((x-y)/2)

Question 8

What are the double angle formulas?

Answer 8

sin(2θ)=2sin(θ)cos(θ)
cos(2θ)=cos^2(θ)-sin^2(θ)=1-2sin^2(θ)=2cos^2(θ)-1
tan(2θ)=(2tan(θ))/(1-tan^2(θ))

Question 9

What are the sum and difference formulas?

Answer 9

sin(x±y)=sin(x)cos(y)±cos(x)sin(y)
cos(x±y)=cos(x)cos(y)∓sin(x)sin(y)
tan(x±y)=(tan(x)±tan(y))/(1∓(tan(x)tan(y)))

Question 10

What are the half angle formulas?

Answer 10

sin(x/2)=±rt((1-cos(x))/2)
cos(x/2)=±rt((1+cos(x))/2)
tan(x/2)=(1-cos(x))/sin(x)

Question 11

What are the laws of sines?

Answer 11

a/sin(a)=b/sin(b)=c/sin(c)

Question 12

What are the laws of cosines?

Answer 12

a^2=b^2+c^2-2bccos(a)

a=cos^-1((b^2+c^2-a^2)/2bc)

Question 13

What are the different equations for the area of a triangle?

Answer 13

(1/2)ab*sin(c)

rt(s(s-a)(s-b)(s-c)) s=(a+b+c)/2

Question 14

What is the equation for the dot product?

Answer 14

u•v=ac+bd=|u||v|cos(θ)

|u|=magnitude of u

Question 15

What are the special case of consistent logs?

Answer 15

log with base a of 1 is always 0

log with base a of a is always 1

Question 16

What is the change of base equation for log

Answer 16

logb(a)=(logx(a))/(logx(b))

Question 17

What are the different logarithm laws?

Answer 17

log(ab)=log(a)+log(b)
log(a/b)=log(a)-log(b)
log(a^b)=b*log(a)
logx((1/(x^a)))=-a
log(x^-1)=log(1/x)=-log(x)

Question 18

What are the different parts and standard forms of a hyperbola?

Answer 18

(((x-h)^2)/a^2)-(((y-k)^2)/b^2)=1
center=(h,k)
vertices=(h±a,k)
foci=(h±rt(a^2+b^2),k)
asymptotes y-k=(±(b/a))(x-h)

(((y-k)^2)/b^2)-(((x-h)^2)/a^2)=1
center=(h,k)
vertices=(h,k±b)
foci=(h,k±rt(a^2+b^2))
asymptotes y-k=(±(a/b))(x-h)
c^2=a^2+b^2

Question 19

What are the different parts and standard forms of a ellipse?

Answer 19

(((x-h)^2)/a^2)+(((y-k)^2)/b^2)=1
foci=(h±rt(a^2-b^2),k) if a>b
foci=(h,k±rt(a^2-b^2)) if b>a
c^2=a^2-b^2

Question 20

What are the different parts and standard forms of a parabola?

Answer 20

y=((1/4p)((x-h)^2))+k if it is a vertical parabola
x=((1/4p)((y-k)^2))+h if it is a horizontal parabola

vertex=(h,k)

focus=(h,k+p) if it is a vertical parabola
focus=(h+p,k) if it is a horizontal parabola
Directrix is the foci flipped about the vertex and is now a line

Question 21

What is de moivre’s theorem?

Answer 21

[r(cos(θ)+isin(θ))]^n=r^n(cos(nθ)+isin(nθ))

Question 22

How do you multiply and divide complex numbers?

Answer 22

r1(cos(θ)1+isin(θ)1)*r2(cos(θ)2+isin(θ)2)=r1r2(cos(θ1+θ2)+isin(θ1+θ2))
r1(cos(θ)1+isin(θ)1)/r2(cos(θ)2+isin(θ)2)=r1/r2(cos(θ1-θ2)+isin(θ1-θ2))

Question 23

How do you find the eccentricity of an ellipse or hyperbola?

Answer 23

e=c/a

Question 24

What equation do you use to find the nth roots of a complex number in the trig form r(cos(θ)+isin(θ))?

Answer 24

((r^1/n)(cos( (θ/n)+((360/n)k) )+(isin( (θ/n))+((360/n)k))

where k=0,1,2,3,…,n-1

Question 25

What is the formula for the average rate of change?

Answer 25

(f(x1+h)-f(x1))/h

Question 26

How do you find the sum of a finite arithmetic sequence?

Answer 26

Sn=((n/2)(a1+an)) or (n/2(2a1+((n-1)d)))

Question 27

What equation do you use to find the nth term of an arithmetic sequence?

Answer 27

an=a1+d(n-1)

Question 28

How do you calculate the sum of a infinite geometric sequence?

Answer 28

a1/(1-r)

Question 29

How do you find the (r+1)th term of (x+b)^n?

Answer 29

(n r)x^(n-r)(y^r)

and if it is the 14th term of the polynomial then r is 13

Question 30

How do you find the sum of a finite geometric sequence?

Answer 30

Sn=(a1(1-r^n))/1-r