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What is the graph of $y = \sin n$ and why is it different from the graph of $y = \sin x$?

I have downloaded a book about Calculus from MIT OCW. In that book, there is a section "A Thousand points of Light". (You can download the relevant section from here.) In that section, it is written ...
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How to draw the graphs for these functions?

Could I please be helped with the graphs for the following functions: $$y=\lceil \tan x \rceil, \quad y=\tan (\lceil x \rceil), \quad y=\lceil \tan (\lceil x \rceil) \rceil$$ I have been able to ...
Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
Is there some systematic way to trace the graphic of $\cos(x) + \cosh(y) = k$ given a fixed value for $k$? Suppose $k = 1$: if I choose empirically $y = 1.2$, I know that should be $\cos(x) = - ... 1answer 16 views Ordering angles using max and min functions I'm using the awesome Desmos Graphing calculator to graph cyclic quadrilaterals. The idea is that the user can drag a slider to change the value of the angle of each point A, B, C and D. I have done ... 0answers 38 views What is the number of x-intercepts in this graph of sine? The function :$y=3-4\sin(2\pi x-3\pi)$.. how many$x$-intercepts over the interval$[0,2]$? I am confused if they're 3 or 5 because there are 3$x$-intercepts that are really intercepting ... 1answer 39 views What's a fast way to sketch$y=\sin (5x) + \frac{3}{10}x \sin (5x)$? What's a fast way to sketch$y= \sin (5x) + \frac{3}{10}x \sin (5x)$? I had this question as part of a recent test paper and I had to sketch it for the range$0 \leq x \leq \pi$. It was for only 2 ... 0answers 38 views How to approach sketching sine and cosine graphs with transformations Any tips or suggestions in sketching these graphs quickly, and in ONE go? In exams, I don't want to spend ages re-drawing the original sine/cosine graph, one by one, following each new ... 1answer 18 views Question about graph of sin function There is question I had on my mind for 3-4 years. If you have a function:- f(x) = (sin(x))^n If you increase the value of n slowly the Value of the function at all points, except where it is one, will ... 1answer 200 views Very interesting graph! I found a VERY interesting graph on http://www.xamuel.com/graphs-of-implicit-equations/. It looked very, very cool, but the equation of the graph is so simple! Here is the image of the graph: My ... 5answers 111 views Rewrite$f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$in the form$f(x) = A \sin (Kx+D)$I got a question like that said "Rewrite$f(x) = 3 \sin (\pi x) + 3\sqrt{3} \cos (\pi x)$in the form$f(x) = A \sin (Kx+D)$". I'm inclined to think that since the periods are the same ($2$), that ... 2answers 68 views Draw the graph of$y=\frac{1}{3}\cos(x)$How can I draw the graph of$y=\frac{1}{3}\cos(x)$with the point along$x$-axis are$0,\pm\frac{\pi}{2},\pm\pi,\pm\frac{3\pi}{2},\dots$. Also show the corresponding points along$y$-axis. 2answers 92 views Formula for solving for Cx and Cy… I'm trying to create a formula to find the third point in a triangle based on two known points and three known sides. Known Sides:$AB, BC, AC$Known Points:$A(x, y), B(x, y)$Unknown Points: ... 3answers 4k views Determine third point of triangle when two points and all sides are known? Determine third point of triangle (on a 2D plane) when two points and all sides are known? A = (0,0) B = (5,0) C = (?, ?) AB = 5 BC = 4 AC = 3 Can someone ... 0answers 95 views Splitting parametric curve equation into two ranges I am examining the speed of motion on curves and in the textbook i am reading , the example was showing that using a parametric equation for an ellipse will result in a regular motion (as expected) , ... 2answers 111 views Several questions about trigonometry and functions [closed] Any help on any of these questions is appreciated. I am studying for my finals and I couldn’t do these questions. Please help. Prove that$\sin^2(x)-6\sin(x)-5=0$has more than one solution for ... 2answers 198 views Evaluate$\cos (-2\pi)$using radiants graph I plotted$2\pi$on the$\cos$graph and the result was$1$, so I assumed$-2\pi$would be$-1$, but it turned out to be$1$. Can someone explain how to work this out? 2answers 116 views How to graph the trigonometric function when period is more than the range? I have to graph this trigonometric equation for a given range,$y = -\sin⁡ \left(\dfrac{x}{3}\right) - 2, ~-\dfrac{\pi}{2} \le x \le \dfrac{\pi}{2}$But the period is coming out to be$6 \pi$. ... 5answers 154 views Graphing$\sin(|x|)$? I'm confused on how the graph is in quadrant II and III. If$|x|$is evaluated first wouldn't all the answers be positive, so that when the range of$|x|$is plugged into$\sin$wouldn't the range of ... 2answers 656 views Why do we use the inverse conversion formula to convert slope per radians to slope per degrees This is a contribution question I'm making in hopes that others may benefit. I will provide my answer underneath. Initially I wanted to ask this question, but I solved it myself and I'd like to give ... 0answers 74 views 3d Implicit Trigonometry help? I'm trying to understand implicit 3D trigonometry, specifically with this equation: $$\sin(y)+\cos(z)=\cos(x)$$ Can someone please explain to me what is going on with this equation? I really can't ... 1answer 172 views Intersection of a point and absolute value function contained within a circle I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point$P$within the circle, ... 1answer 320 views How are the parametric equations describing the cupid curve derived? [duplicate] No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages ... 4answers 803 views Romantic Math Equations [closed] Try the following in Google: sqrt(cos(x))*cos(300x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(6-x^2), -sqrt(6-x^2) from -4.5 to 4.5 Are there any other interesting ... 2answers 88 views What is the equation that fits this curve? I have a curve that looks like this (it's cyclical): Curve I can get a partial fit by fitting a 3rd degree polynomial, but I have a feeling there must be a better fit (something that involves sin ... 1answer 1k views General Cartesian/Rectangular Equation for Polar Rose ($r=\sin(k\theta)$) How do I convert the Polar Equation$r=\sin(k \theta)$to Cartesian Equation? I understand that$r^2=x^2+y^2$and that$x=r\cos\theta$and$y=r\sin\theta$, but no matter how I try to arrange them it ... 1answer 336 views How to find the limit of$\sin(f(x))$, given the graph of$f(x)$The full question is uploaded here: http://imgur.com/EZekb Basically, given the graph shown in the image above, I thought that the limit of$\sin(f(x))$would be$\sin(2)$, since the limit of just ... 2answers 76 views How to obtain more than two abcissas for one ordinate? I'm reading a book on trigonometry and the author shown that some of the examples contain one abcissa for one ordinate and he showed that a parabola has two abscissas for every positive ordinates, I ... 2answers 194 views OCR: some App to calculate the derivative on a line graph with iPhone/iPad? Problem I have a set of points like the ones shown on the right hand side of the image. So for each 'Ships Head' there is a corresponding value for 'Deviation'. In this example we can treat west ... 1answer 104 views How to graph this? I have a non-right triangle. I will call the bottom or base edge$b$, the top left edge$a$, the top right edge$c$. Let$ a=c+2 $and$b=10$. How do I graph a curve where the ... 5answers 1k views Why aren't the graphs of$\sin(\arcsin x)$and$\arcsin(\sin x)$the same? (source for above graph) (source for above graph) Both functions simplify to x, but why aren't the graphs the same? 1answer 159 views Sketching graph Exponential and logarithmic functions. Sketch the graph of each of the following (labelling asymptotes), and state the range of each:$y=3^x+1$is below graph. I have no idea, how can it get$(0,2)$i know that the$+1$is asymptotes, ... 1answer 77 views Draw$\cos2\pi10t$on graph How do I draw this graph? Eg.$\cos\pi$starts at y=1, flows down to x=$\pi$as the mid point where y=-1 and goes back to y=1. I'm not sure how to decipher the$2\pi10t$here and put them into ... 1answer 223 views polar graphs and investigation I am new to polar graphs and I am trying to investigate some certain cases: What happens when you change the$b$value to different positive integers in polar equations of the forms: ... 1answer 59 views Does the area of web chart diagrams depend on the order of items? I am trying to discourage people from using radar chart diagrams (e.g. this one) where this is not appropriate. I have already made the point that the optical effect will be distorted because ... 6answers 568 views Intuitive Explanation of the graph$y = \sin x$[duplicate] Possible Duplicate: Intuition for graphing Sine/Cosine We've all seen the graph of$y = \sin x$(I can't post an image because of reputation so I posted a link to a graph) Sine Graph ... 2answers 205 views Can you explain why plotting$\cos(\cos(90 \sqrt{x}))$looks like this? Can you explain why plotting$\cos(\cos(90 \sqrt{x}))$looks like this: (from here) 1answer 880 views Combining Sine Waves on Chart I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the ... 2answers 100 views How to graph equation So the problem is to find all points$(x,y)$on the real plane such that$f(x,y) = \cos^2(x+t) + 2\sin(x+t)\cos(y) - \frac{(\cos y - 1)^2}{2} - \sin(x) \lt .5$for all real$t$. I'm not sure where to ... 1answer 240 views Graph for$f(x)=\sin x\cos x\$
Okay, so in my math homework I'm supposed to draw a graph of the following function: $$f(x)=\sin x \cos x.$$ I have the solution in the textbook, but I just can't figure out how they got to that. So, ...