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  3. 1 all points with coordinates cos and yrsin where r...

Question: 1 all points with coordinates cos and yrsin where r...

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1. All points with coordinates cos() and yrsin(), where r is a constant, lie on a circle with radius r, i.e. satisfy the equation r2 + y2 -r2 Create a row vector for θ with the values-0, , , , Taker 6 and compute the row vectors z and y Now check that r and y indeed satisfy the equation of a circle, by computing the radius 부厝and Hint: To calculate r you will need the array operator could also compute z2 by x. for squaring r andy. Of course, you 2. Use the linspace command or the colon operatorto create a vector t with entries i, to suppress /10 cos2 (make sure you use 0.3t313 4,4.2,4.4,..., 20, and define the functiony- the output for both t and y) (a) Plot the function y in black and include a title with the expression for y (b) Make the same plot as in part (a), but rather than displaying the graph as a curve, show the unconnected data points. To display the data points with small circles, use plot(t,y, Now combine the two plots with the command plot (t,y, o-) to show the line through the data points as well as the distinct data points. 3. Use the command plot3(x,y,z) to plot the circular helix r 4 cos(3t), y 4sin(3t), z 2t, 0ts 10. Add a grid to the plot using the command grid on. NOTE: Use semicolon to suppress the output when you define the vectors t, z, y and z. Make sure you use enough points for your graph so that the resulting curve is nice and smooth. 4. Plot y sin(7a) in red with a solid line and the Taylor polynomial approximation z 7- ,3 in blue with a dashed line for-恥エ on the same plot. Hint: Use plot(x,y,r,x,z,--) Add a grid to the plot using the command grid on. Type axis tight to set the axis limits to the range of the data. NOTE: Use semicolon to suppress the output when you define the vectors r, y and z. Make sure you use enough points for your graph so that the resulting curves are nice and smooth.The gearral slution to 11 e dillitutial equation dy--lz-17r + 8cow(z) įs 1 17 lx) The gual hircise is to write aacript lile to plot the solutios to the dilfrential ation in the inval Os S 4, with initial conditions ylo)-80, 13, 190 Example 2, page ) Call theile Tlae Sumetion that delins vz) be included in he same Se (note that the uetion delining x) will hane two input argument and C). Your M-lile sould have thae Sollowing structure(in all the with he appeopriate cm- . ?? ; % defina tha vector in tha i ter val [0,4] yi £(??); % compute tha aolution with C 80 y2 . f(??); % compute tha aolution with C- 130 y3 . f(7?) ; % compute tha aolution with C 190 plot(??) % plot the three aolutiona with different lin -aty1ea title(??) %adda title legend (??) % add a lagand funetion y-(,c) y . ?? % fill.is with the espreaa ion for tba gozeral aolution Plot the gpl in the sae window and use dillerent color andfor line-stylas Sor esc grapi. To plot the graphs in thesm windo you can the cmnd hold an oee the plot c similaly to Eei 4 Addhe title Solutions to du/ds--1-17+8() Add a legend with the C vls ed Sor esch graph (Type balP Plet โยเเ โ1 cd the dilleretzl lina-tylas, aand balP 1.gend fr helpen how to MII a legetul.) Include bath the M-lile and that plut in your ะ.Fort. NOTE: the nly output of the seript lile lhould he he graph of the thae cwves Make sure 6. (a) Eate the functica glv)- s an anonymous bction(ee pages 6 and 7). Evaluate the fundan al 1-1 and F--2 ly mlirizgg(1, -2) İn the eumauuul b) Type clear g to the value of the umetioa from part (a). Now wite a unctio Saetee a g-- (include teM-ile in your report) Evaluate the functiona at- and 2 by en 1-2) in be command

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