Trigonometry identities
I am the most fundamental of all trigonometric identities, derived directly from applying Pythagoras's theorem to the unit circle.
What is sin^2x+cos^2x=1
I am the function y=sinx after is has been dilated vertically by a factor of 3
What is y=3sinx
I am the general equation form of any relationship described a directly proportional.
What is y=kx
The set of all point equidistant from a point and a line. I am a well known curve used in satellite dishes and head lights due to the focal point I create.
What is a parabola
d/dx xsinx
What is xcosx+sinx
I am a dimensionless quantity that tells you the precise number of standard deviations a raw score is away from the mean of its distribution. A positive value for me always means the score is above average.
What is a Z-score
int x(x^2+1)^3dx
int x(x^2+1)^3dx=1/8(x^2+1)^4+C
tan^2x+1
sec^2x
I am the function y=cosx but my period is half as long.
What is y=cos(2x)
Though I am born from an infinite process, and I resolve into a single, finite number, but only if that process is one of decay, not growth.
What is the limiting sum of a geometric series
With rotational symmetry around my single point of inflexion. I can be an odd function but never an even function.
What is a cubic
d/dx ln(x^3+4)
What is (3x^2)/(x^3+4)
In a group of 100 students, 40 are studying Physics, 30 are studying Chemistry, and 10 are studying both. I am the probability that a student is studying Physics, given that they are studying Chemistry.
What is 1/3
intsin(2x)dx
-1/2cos(2x)+C
cos(pi/2-theta)
What is sintheta
I am a sine function with a period of 4pi and a amplitude of 5
What is y=5sin(1/2x)
I am the storyteller of data, describing the relationship between two characters. I can tell you if they move together, in opposition, or not at all, but I am famous for my one limitation: I can never prove that one caused the other.
What is correlation
With two asymptotes. I am composed of two distinct, symmetrical branches.
What is a hyperbola
d/dx lnx/x as a single term
What is (1-lnx)/x^2
I am a statistical rule which states that for a normal distribution almost all observed data will fall within three standard deviations of the mean.
What is the Empirical rule
int_1^e1/xdx
int_1^e1/xdx=1
(sinx-1)(sinx+1)
What is the -cos^2x
Beginning as the function y=sinx , after a phase shift of pi/2 to the right I am now completely different function.
What is y=-cosx
I am a system of functions defined by a cyclical relationship of derivatives. This recursive property makes me the fundamental language of all oscillations.
What is Trigonometry
The rate at which I grow is proportional to my current value. For a particular constant I am my own derivative.
What is an exponential
d/dx 10^(x^2)
What is 2x(ln10)10^(x^2)
I am the value of the constant, k, the makes the function f(x)=kx a valid probability density function over the interval for x=0 to x=4.
k=1/8
int cosx/(1+sinx) dx
int cosx/(1+sinx) dx=ln(1+sinx)+C
sinx/(1+cosx)+cotx
cosec x
I am a cosine function with a maximum value of 1 and minimum value of -5. I have a maximum point located at (pi/2,1) and the next consecutive maximum at ((5pi)/2,1)
What is y=3cos(x-pi/2)-2
I embody the paradox that an infinite process of finding a function's total accumulation can be resolved by examining only its start and end, thereby uniting the continuous with the discrete.
What is integral calculus
I have one or more points at which I am not differentiable due to the occurrence of a vertex at these important values.
What is an absolute value graph
I am the x-coordinate of the single stationary point on the curve defined by the function y=xe^(-2x)
What is x=1/2
Events A and B are mutually exclusive events of a sample space with P(A)=p and P(B)=q where 0<p<1 and 0<q<1 .
P(A'nnB') is equal to
P(A'nnB')=1-p-q=1-(p+q)
int_0^(pi/12)sec^2(3x)dx
int_0^(pi/12)sec^2(3x)dx=1/3