Math 118: Assignment 10 SolutionsNOT TO BE HANDED IN(this is for practice)1. Sketch the curve of the parametric equationsx=sec2t-1y=tantfor 0≤t≤π/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 0≤t≤2πis called theLissajous curve.(a) Determine all thexandyintercepts.(b) Use derivatives to determine the points where the curve has horizontal tangent linesand vertical tangent lines.