Cosecant Function

 A tutorial on exploring the cosecant function given by f(x) = a * csc( b x + c ) + d and its period, phase shift, asymptotes domain and range is presented. An interactive applet is used where parameters a, b, c and d are changed and their effects explored. Interactive Tutorial Your browser is completely ignoring the tag! 1 - Click on the button above "click here to start" and maximize the window obtained. 2 - Use the scroll bar to set a = 1, b = 1, c = 0 and d = 0. Now change a , how does it affect the graph? Does it affect the range? If yes how? 3 - Set a = 1,c = 0,d = 0 and change b. For each value of b find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)? How does it affect the asymptotes? 4 - Set a = 1,b = 1,d = 0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to - c / b. 5 - Set a = 1, b = 1, d = 0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to - c / b. 6 - Repeat 4 and 5 above for b = 2, 3 and 4. 7 - Set a,b and c to non zero values and change d. What is the direction of the shift of the graph? 8 - Which of the parameters affect the positions of the asymptotes (in red)? Explain analytically. 8 - Which of the parameters affect the domain of the cosecant function? Explain analytically. 9 - Which of the parameters affect the range of the cosecant function? Explain analytically. More references on the trigonometric functions. Trigonometric Functions.