M-172Q Quiz: MATH 172 Montana State Quiz11

7. (10 pts) Consider the parametric curve given by x(t) = 2t-sin(2t), y(t) = 1-cos(2) for t E [0, (a) Compute the slope of the tangent at the point where t = π/5 (b) For which t E [0, π] is the tangent horizontal?

1. Write the equation of the hyperbola. Center: (0, 0) Vertex: (0, 3) Focus: (0, 6 2. Convert from parametric to rectangular Parametric Equations: x = 6 cos θ , y = 6 sin θ 3. Sketch the curve represented by the parametric equations (indicated the the curve), and write the corresponding rectangular equation. Param etric Equations: x = t-6 , y = t2 d2y 4, Find and and find the slope and concavity (if possible) at the give parameter. Parametric Equations:--, y = t 2 Parameter: t=-2 r = 2sin 5. Sketch a graph of r 5 cos 6. Find the Cartesian coordinates of the points b. (2,r/3) Figure A 7. Find the area of the region described below and pictured in Figure A. The region bounded by the circle r-2 sin θ for- 6S π/2.

3. +-15 points SCalcET8 10.1.AE.002 My Notes Ask Your Teacher EXAMPLE 2 equations? What curve is represented by the following parametric x = 4 cos(t) y = 4 sin(t) 0 t 2n (4 cos(t), 4 sin(t)) SOLUTION If we plot points, it appears that the curve is a circle. We can confirm this impression by eliminating t. Observe that x2 + y2 = 16 cos2(t) + 6 Thus the point (x, y) moves on the circle x2 + y2- . Notice that in this example the parameter t can be interpreted as the angle (in radians) shown in the figure. As t increases from 0 to 27, the point (x, y) = (4 cos(t), 4 sin(t)) moves once around the circle in the -Select 4direction starting at the point (x, y) = Video Example Need Help?Read It Talk to a Tutor