# Assignment 10 with solutions - Math 118 Assignment 10...

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Math 118: Assignment 10 SolutionsNOT TO BE HANDED IN(this is for practice)1. Sketch the curve of the parametric equationsx=sec2t-1y=tantfor 0tπ/3.Indicate the direction with arrows on the curve.Hint: First write theequation in terms ofxandyfor this curve.
2. Given our interval fortwe see that (x, y) runs from(0,0) to (3,3) in the first quadrant (sincey= tan(t) is positive whentis between 0 andπ3). This gives us the top half of the parabola as shown below2. The curve of the parametric equationsx=sinty=sin (2t)for 0t2πis called theLissajous curve.(a) Determine all thexandyintercepts.(b) Use derivatives to determine the points where the curve has horizontal tangent linesand vertical tangent lines.
(c) Sketch the graph. Indicate the direction with arrows on the curve.Solution:
3. Find the total distance travelled by a particle along each of the following paths.(a)x= 3t2, y=t3,-1t1(b)x=et-t, y= 4et/2, 0t1Solution: