Concept explainers
Arc Length In Exercises 49-54, find the arc length of the curve on the given interval.
Parametric Equations Interval
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 10 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.arrow_forwardUse point plotting to graph the plane curve described by the given parametric equation x = -sin t, y = -cos t; 0 ≤ t < 2π. Use arrows to show the orientation of the curve corresponding to increasing values of t.arrow_forwardUse a graphing utility to graph the curve represented by the parametric equations Prolate cycloid: x = 2θ − 4 sin θ, y = 2 − 4 cos θ . Indicate the orientation of the curve. Identify any points at which the curve is not smooth.arrow_forward
- Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve x = 3 cos(Θ) , y = sin(Θ)arrow_forwardUse a graphing utility to graph the curve represented by the parametric equations Cycloid: x = θ + sin θ, y = 1 − cos θ. Indicate the orientation of the curve. Identify any points at which the curve is not smooth.arrow_forwardUse a graphing utility to graph the curve represented by the parametric equations. Indicate the direction of the curve. Cycloid: x = 5(? − sin(?)), y = 5(1 − cos(?)) and Identify any points at which the curve is not smooth. EXPLQIN AND MARK THE ANSWERS IN AN BOX THANKSarrow_forward
- Graph the curve with parametric equations x = sin(t), y = 2 sin(2t), z = sin(3t). And Find the total length of this curve correct to four decimal places. Calculus 3arrow_forwardConsider the parametric curve = cos(t) sin(t) and y sin²(t) on the domain () < t < π. = Find the values of t for which this function has a horizontal tangent line. Find the values of t for which this function has a vertical tangent line. Question Help: Message instructor Submit Questionarrow_forwardA pair of parametric equations is given. x = cos?(t), y= sin?(t) (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. y y 0.5/ 1.5 1.0 -1.5 -1.0 -0.5 0.5 -0.5 0.5 -1.0 -1.5 -1.0 -0,5 0.5 -0.5 -1.5 0.5 1.5 -0.5 1.0 0.5 1.0 1.5 -0.5 0.5 -1.0 -0.5 0.5 1.0 1.5 -15 -0.5 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter. wherearrow_forward
- Use a graphing utility to graph the curve represented by the parametric equationsHypocycloid: x = 3 cos3 θ, y = 3 sin3 θ . Indicate the orientation of the curve. Identify any points at which the curve is not smooth.arrow_forwardUse a graphing utility to graph the curve represented by the parametric equations. Indicate the direction of the curve. Cycloid: x = 3(0 – sin(0)), y = 3(1 – cos(0)) - y y 6 6 5- -5 4 -4 3 10 15 -20 -15 -10 -5 7 10 15 y 6 4 -4 -5 -6 y 10 15 Identify any points at which the curve is not smooth. O The graph is smooth everywhere. The graph is not smooth at 0 = nn. The graph is not smooth at e = -nt. The graph is not smooth at e = 3nn. The graph is not smooth at 0 = 2nn.arrow_forwardParametric equation x = 4 + 2 cos t, y = 3 + 5 sin t; t =π/2 and a value for the parameter t are given. Find the coordinates of the point on the plane curve described by the parametric equation corresponding to the given value of t.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)