Hacking Math | The worlds fastest way to learn mathematics.

Start with a graph that has a radius of $3$ you know how this graph looks like it's just a circle with a radius of $3$ »

Graphing the trigonometric functions can be a bit tricky especially if you are going to be doing this by hand. I'm going to be showing you »

The phase shift of a graph determines if the graph is going to be shifted left or right on the x-plane of the graph. $$Asin[B( »

The period of a trigonometric function is closely related to the frequency of the function. They are related but not the exact same thing. Period vs »

The frequency is closely related to the period of the base trigonometric functions. Since we are using the definition of the length of the given circle »

To find the vertical shift of a trigonometric function you will need to take a close look at the function that you are viewing. Let's start »

The amplitude of a trig function defines how much the graph is going to be getting stretched or compressed on the y-axis. Take for example the »

This is the most basic of an idea but it's an important idea that you need to understand to be able to comprehend higher levels of »

table { font-family: arial, sans-serif; border-collapse: collapse; width: 100%; } td, th { border: 1px solid #dddddd; text-align: left; padding: 8px; } $Degrees$ $Radians$ $sin(x)$ $cos(x)$ $tan(x) »

This post is not going to be about how to use your fingers or sing a song to memorize the common trigonometric angles. Instead of having »

A right triangle is a triangle that contains one right angle and two acute angles which all add up to $180°$ degrees. $$right\ angle=90°$$ $$acute\ »

Question: The Giant Wheel at Cedar Point Amusement Park is a circle with diameter 128 feet which sits on an 8 foot tall platform making its »

The circumference of a circle is the length that composes a circle. If you were to undo a circle and lay it down as a flat »

Linear speed is how fast the arc of any given angle is growing. This is useful to determine the linear speed with the relationship to time. »

To find any given theta angle you will need to know the arc length and the radius. Any given angle gives the rise to the arc, »

Angular speed is how fast the central angle changes in respect to time. Below you will see an angle that is changing by $\theta$ distance. With »

Two acute angles that equal to the sum of 90 degrees are complementary angles. $$\alpha =90°-\beta$$ »

The DMS system also referred to as Degree-Minutes-Seconds is a system that is typically used by surveying a position that requires longitude and latitude. In the »

The DMS system also referred to as Degree-Minutes-Seconds is a system that is typically used by surveying a position that requires longitude and latitude. In the »

A ray is created based on an initial point and expanded out to n length. »

Acute Angle $$cos(x)>0\Rightarrow 0°< x < 90°$$ Obtuse Angle $$cos(x)<0\Rightarrow 90°< x <180°$$ »

Here is a list of degrees to radians conversions that you need to have memorized. You need to be able to recite each one of this »

The function tan(x) $$tan(x)=\frac { opposite }{ adjacent }$$ The inverse of the function $$tan(x)=\frac { adjacent }{ opposite }$$ Or you can also represent tan(x) »

The function cos(x) $$cos(x)=\frac { adjacent }{ hypotenuse }$$ The inverse of the function $$sec(x)=\frac { hypotenuse }{ adjacent }$$ »

The function sin(x) $$sin(x)=\frac { opposite }{ hypotenuse }$$ The inverse of the function $$csc(x)=\frac { hypotenuse }{ opposite }$$ »

The follow triangle shows the relationships between $x$ and the relating sides. Soh $$sin(x)=\frac { opposite }{ hypotenuse }$$ Cah $$cos(x)=\frac { adjacent }{ hypotenuse }$$ Toa $$tan( »

To convert degrees to radians you will need to multiply degrees by pi and divide by 180. $$f(x)=\frac { \pi (x) }{ 180 } $$ »

To convert radians to degrees you will need to multiply the radians by 180 and divide by pi. $$ f(x)=\frac { 180(x) }{ \pi } $$ »

$$1°=\frac { 1 }{ 360 }$$ »

$$ y-{ y }{ 1 }=m(x-{ x }{ 1 }) $$ »

A radian is a unit measurement of an angle. $$2\pi = 360°$$ $$\pi = 180°$$ $$1radian=(\frac { 180 }{ \pi } )\approx 57.3°$$ »

An angle is composed of three different parts. Vertex Terminal Initial Side »

This single one image shows you every single relationship from a triangle to a circle and the lines that join both of this shapes together. »

Finding the vertical asymtote is the easiest at of all them. Yes! Don't make a big deal out of it it's simple. To locate the vertical »

Finding the horizontal asymtote is a bit more tricky then just the simple vertical asymtote. You have to take to consideration a couple of things before »

You have 200 yards of fencing and wish to enclose a rectangular area. Create a function such that it expresses width of the rectangular area. The »

$$\frac { rise }{ run } =\frac { Δy }{ Δx } =\frac {y2-y1}{ x2-x1 }$$ »

To determine if a factor is part of a given equation you have to find out if the devision of that factor by the polynomial will »

Find the equation of a hyperbola with following characteristics. $$Origin: (0,0)\ Focus: (3,0)\ Vertex: (-2,0)$$ a is the distance from the origin of »

Hyperbola is a collection of all points in a plane, where the difference of the distance from two fixed points is the foci is a constant. »

Find the equation of an ellipse with the following. $$Center: (0,0)\ Focus: (3,0)\ Vertex: (-4,0)$$ a is the distance from the origin of »

An ellipse is a collection of all points in a plane which the sum of two fixed points is called the foci a constant. Using the »

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To analyze an equation of a parabola their special characteristics that can be looked at to determine what type of parabola it is. Example: Let's get »

Find the equation of the parabola: Before getting started with the algebra the problem provides the following information. Focus: (-4,0) Vertex: (0,0) Now let's »

To figure out the equation of a parabola we must first understand what is a parabola? The equation of a parabola has to have the following. »

A parabola is a collection of a all points in a plane that are the same distance from a fixed point as they are from a »

When working with logarithmic equations think about each one as a representative of and exponential equation because it is it's inverse. Example: »

To solve exponential functions you must first get the equation to be the same base left and right in the LOWEST POSSIBLE BASE. Example »

1.The domain is the set of all real numbers, and the range is the set of positive numbers 2. There are no x-intercepts; the y »