please calculate me 1, 2, 3, 4, 5. Please write clearly for me. Thanks.

Calculus II: 25 Parametric curves \"prism: 7h ago All lessons due next Wednesday, 11:00pm - in 4 days Live Notes ElEXPand A11 PDF-beta . One of central themes in calculus is the study of the shapes of graphs of curves 3; = f (I). In this lesson we describe a new method for discribing curves by using a third variable called a parameter. Such descriptions are natural and they are common in physics. For example, each of the two coordinates of a particle moving in the plane an be given as functions of time. Example - The unit CiI'CIE. Consider familiar equations: x 7 cos I, y r sin I, [:JMango' Homework PDF-beta . 1. Discuss, share but do not submit: Find good graphical calculators on the internet that can plot parametric curves. Then plot: a: = t/2 y = sint. and a: = tcost, y = tsint. 2. Find parametric equations for the upper semi circle with center (4, 3) and radius 5. Sketch such this semicircle rst. 3. Eliminate the parameter to nd a Cartesian equation of the curve. a: = 63' y = t + 1. 4. Find the points on the curve at = cost, y = 251nt,0 S t S 277. at which the tangent is a) horizontal, b) the tangent is vertical. What is the name of this curve? 5. Find the tangent of the cycloid x = r(t sin t), y = r(1 cost) at the point where t = vr/3