Equations Flashcards
What is an even function?
It is a function that is symmetric about the y axis
What is an odd function?
It is a function that is symmetric about the origin
What is the equation for continuous compounding?
A=P(e^rt)
What are the pythagorean identities?
sin^2(θ)+cos^2(θ)=1
tan^2(θ)+1=sec^2(θ)
1+cot^2(θ)=csc^2(θ)
What are the even and odd identities?
sin(-x)=-sin(x)
cos(-x)=cos(x)
tan(-x)=-tan(x)
What are the product to sum formulas?
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)]
What are the sum to product formulas?
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)
What are the double angle formulas?
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))
What are the sum and difference formulas?
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)))
What are the half angle formulas?
sin(x/2)=±rt((1-cos(x))/2)
cos(x/2)=±rt((1+cos(x))/2)
tan(x/2)=(1-cos(x))/sin(x)
What are the laws of sines?
a/sin(a)=b/sin(b)=c/sin(c)
What are the laws of cosines?
a^2=b^2+c^2-2bccos(a)
a=cos^-1((b^2+c^2-a^2)/2bc)
What are the different equations for the area of a triangle?
(1/2)ab*sin(c)
rt(s(s-a)(s-b)(s-c)) s=(a+b+c)/2
What is the equation for the dot product?
u•v=ac+bd=|u||v|cos(θ)
|u|=magnitude of u
What are the special case of consistent logs?
log with base a of 1 is always 0
log with base a of a is always 1
What is the change of base equation for log
logb(a)=(logx(a))/(logx(b))
What are the different logarithm laws?
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)
What are the different parts and standard forms of a hyperbola?
(((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
What are the different parts and standard forms of a ellipse?
(((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
What are the different parts and standard forms of a parabola?
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
What is de moivre’s theorem?
[r(cos(θ)+isin(θ))]^n=r^n(cos(nθ)+isin(nθ))
How do you multiply and divide complex numbers?
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))
How do you find the eccentricity of an ellipse or hyperbola?
e=c/a
What equation do you use to find the nth roots of a complex number in the trig form r(cos(θ)+isin(θ))?
((r^1/n)(cos( (θ/n)+((360/n)k) )+(isin( (θ/n))+((360/n)k))
where k=0,1,2,3,…,n-1
What is the formula for the average rate of change?
(f(x1+h)-f(x1))/h
How do you find the sum of a finite arithmetic sequence?
Sn=((n/2)(a1+an)) or (n/2(2a1+((n-1)d)))
What equation do you use to find the nth term of an arithmetic sequence?
an=a1+d(n-1)
How do you calculate the sum of a infinite geometric sequence?
a1/(1-r)
How do you find the (r+1)th term of (x+b)^n?
(n r)x^(n-r)(y^r)
and if it is the 14th term of the polynomial then r is 13
How do you find the sum of a finite geometric sequence?
Sn=(a1(1-r^n))/1-r
