Sinθ vs Cosθ The sinθ wave begins with at the origin, while the cos θ graph begins at (0,1) with the vertex at x=0.
Cscθ Period: 360° Amplitude: 1 The asymptotes of csc θ are where they are because the inverse of infinity, negative infinity, and zero do not exist, so wherever sin θ is zero, scs θ does not exist.
Secθ Period: 360° Amplitude: 1 The asymptotes of sec θ are where they are because the inverse of infinity, negative infinity, and zero do not exist, so wherever cos θ is zero, sec θ does not exist.
Tanθ Period: 360° Amplitude: 1 The asymptotes of tan θ are where they are because infinity and negative infinity are not real numbers.
Cot θ Period: 360° Amplitude: 1 The asymptotes of cot θ are where they are because the inverse of zero does not exist, so wherever tan θ is zero, cot θ does not exist.
void loop () { while (k<2000){ for (int x=0;x<180;x++) { sinVal = (sin(x*(3.1412/180))); toneVal=2000+(int(sinVal*1000)); tone(8.toneVal); k++; delay(2); }}
for (int x=0;x<180;x++) { sinVal = (sin(x*(3.1412/180))); toneVal=2000+(int(sinVal*1000)); tone(8,toneVal); delay (5); } } To change the tone of the siren, we changed the number in the sinVal perenthases. To make it loop and change every five seconds, we set the delay to five.
A UNIT CIRCLE THAT'S ACTUALLY READABLE (They say the same thing)
HOW TO USE A UNIT CIRCLE: These unit circles show three things- 1. The (x,y) locations of individual points that would be on two special kinds of triangles if you were to set one on the circle with the smallest angle of the triangle at the point of reference. 2. The distance, in radians, from zero to the location of the angle. And the angle itself. When given a problem that asks you to find one of those three things
Federal/Government: has typically lower fixed interest rates and income-based repayment plans, you don't have to pay for them until you're out of school, don't always need a credit check to get these, interest can be tax deductible, sometimes possible to postpone payments.
Subsidized - you don't gain interest while you're in school (the government pays for it).. unless there's a forbearance CURRENT INTEREST RATE: 4.66% (undergrad)
Unsubsidized - gains interest while you're in school CURRENT INTEREST RATE: 4.66% (undergrad)
Private/Bank: more expensive, higher interest rates that can change, payment isn't based on income, normally have to pay while you're in school, normally need a credit check first CURRENT AVERAGE INTEREST RATE: 10.52%
In order to fold a normal piece of computer paper enough times for it to go to the moon, one would have to fold it in half 42 times. Of course, this is impossible (any piece of paper can only be folded in half up to about seven times due to the amount of force needed to fold it with the decreasing surface area and increasing thickness). If it were possible, the area of the paper when it finally got to the moon would be about 0.00000000002 square inches; so, microscopic.. and impossible..
Limits are a horizontal or vertical line on a graph that a function does not cross or touch. You can tell that a limit exists if you plug a number into a function and the answer doesn't exist. Limits help us explain function behavior at points of discontinuity by allowing us to explain what is happening to the function on either side of the discontinuity.
By graphing an equation, we are able to see the "easy zeros," and we can then use them to find any other zeros (if there is any). The highest power of the equation tells us how many zeros the equation has, and, in turn, how many factors it has because the number of zeros and the number of factors are the same. If we set the zeros equal to x and solve, we find the factors of an equation. Although, sometimes there is some zeros that aren't as easy to identify, such as imaginary zeros and square root zeros. These ones can be found through division by dividing the entire equation by the easy zeros until you are left with a polynomial function, then setting it equal to zero and solving.
I got this function by combining three other functions and limiting their domain and range so that they only went to where they were supposed to be. These functions included (from left to right) a linear function, a circle function, & a parabolic function
The way to find the inverse of a function is to input y wherever there is an x, and put x wherever there is a y then solve for y. Also, the inverse of functions is graphed as a reflection over the axis y=x. Even though my graph didn't completely match up when I folded the plastic sheet through the y=x axis, that's how it's done.. It's only crooked because I didn't do a very good job drawing the parabolas. I think that some functions that can have inverses that are also functions; not parabolas though.