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Wikispace Final Project Opposite of y=sin(x) To graph: 1.)First graph the function as sine. 2.) Draw asymptotes where it crosses the xaxis. 3.) Graph the opposite of sine by drawing a flipped parabola at the graphs amplitude. EXAMPLE: *Purple parabolas represent the csc(x)* http://jwilson.coe.uga.edu/EMT668/EMAT 6680.2000/Umberger/EMAT6690smu/Day 6/Resources/cosecant.gif Opposite of y=cos(x) To graph: 1.) First graph the function as cosine 2.) Draw asymptotes where it would or does cross the x-axis. 3.) Since it is split into three parts due to the asymptotes: the first and third section; draw lines leading towards the asymptotes. For the middle section draw a parabola opposite of the point of its amplitude. EXAMPLE: Section 1 Section 3 Section 2 http://fouss.pbwiki.com/f/sec%20x. jpg Opposite of y=tan(x) Best drawn alone without the help of its opposite [y=(tan)x]. Asymptote at 0 and π (changes depending on the extent of the problem) To graph: Put midpoint of the function in between the two asymptotes, then flip the graph opposite of what it would be if it were tangent. The graph is the same shape as EXAMPLE: tan(x), but it is reversed http://www.intmath.com/Trigonometricgraphs/cotx.gif Similarities ◦ All flipped ◦ All have asymptotes ◦ All are forms of Trig Functions Differences ◦ For Cosecant and Secant: Graph Sine and Cosine first, then draw its function ◦ For Cotangent: Best to memorize both the funtion of tan(x) and cot(x)