Precalculus: Mathematics for Calculus (Standalone Book)
7th Edition
ISBN: 9781305071759
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Brooks Cole
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Question
Chapter 8.4, Problem 50E
To determine
The graph of parametric equations.
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Chapter 8 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
Ch. 8.1 - We can describe the location of a point in the...Ch. 8.1 - Prob. 2ECh. 8.1 - Yes or No? If No, give a reason. 3. Do the polar...Ch. 8.1 - Yes or No? If No, give a reason. 4. Do the...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Polar Coordinates to Rectangular Coordinates A...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Prob. 69ECh. 8.1 - Prob. 70ECh. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.2 - To plot points in polar coordinates, we use a grid...Ch. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Rectangular to Polar Sketch a graph of the...Ch. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Orbit of a Satellite Scientists and engineers...Ch. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.3 - A complex number z = a + bi has two parts: a is...Ch. 8.3 - Let z = a + bi. (a) The modulus of z is r =...Ch. 8.3 - (a) The complex number z = 1 + i in polar form is...Ch. 8.3 - How many different nth roots does a nonzero...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - A Complex Number and Its Modulus Graph the complex...Ch. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Graphing a Complex Number and Its Complex...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Graphing Sets of Complex Numbers Sketch the set in...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Graphing Sets of Complex Numbers Sketch the set in...Ch. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Polar Form of Complex Numbers Write the complex...Ch. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Polar Form of Complex Numbers Write the complex...Ch. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.3 - Prob. 65ECh. 8.3 - Prob. 66ECh. 8.3 - Prob. 67ECh. 8.3 - Prob. 68ECh. 8.3 - Prob. 69ECh. 8.3 - Prob. 70ECh. 8.3 - Prob. 71ECh. 8.3 - Prob. 72ECh. 8.3 - Prob. 73ECh. 8.3 - Prob. 74ECh. 8.3 - Prob. 75ECh. 8.3 - Prob. 76ECh. 8.3 - Prob. 77ECh. 8.3 - Roots of Complex Numbers Find the indicated roots,...Ch. 8.3 - Prob. 79ECh. 8.3 - Prob. 80ECh. 8.3 - Prob. 81ECh. 8.3 - Prob. 82ECh. 8.3 - Prob. 83ECh. 8.3 - Prob. 84ECh. 8.3 - Prob. 85ECh. 8.3 - Prob. 86ECh. 8.3 - Prob. 87ECh. 8.3 - Prob. 88ECh. 8.3 - Prob. 89ECh. 8.3 - Prob. 90ECh. 8.3 - Prob. 91ECh. 8.3 - Prob. 92ECh. 8.3 - Prob. 93ECh. 8.3 - Prob. 94ECh. 8.3 - Prob. 95ECh. 8.3 - Prob. 96ECh. 8.3 - Prob. 97ECh. 8.3 - Prob. 98ECh. 8.3 - Prob. 99ECh. 8.3 - Prob. 100ECh. 8.3 - Prob. 101ECh. 8.4 - (a) The parametric equations x = f(t) and y = g(t)...Ch. 8.4 - (a) True or False? The same curve can be described...Ch. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 14ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 17ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 19ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Sketching a Curve by Eliminating the Parameter A...Ch. 8.4 - Prob. 27ECh. 8.4 - Circular Motion The position of an object in...Ch. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Prob. 33ECh. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Parametric Equations for Curves Find parametric...Ch. 8.4 - Prob. 37ECh. 8.4 - Path of a Projectile Referring to Exercise 37,...Ch. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Prob. 52ECh. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prolate Cycloid (a) In Exercise 55 if the point P...Ch. 8.4 - Parametric Equations of a Hyperbola Eliminate the...Ch. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Prob. 62ECh. 8.4 - Hypocycloid A circle C of radius b rolls on the...Ch. 8.4 - Prob. 64ECh. 8.4 - Longbow Curve In the following figure, the circle...Ch. 8.4 - Prob. 66ECh. 8.4 - Eliminating the Parameter Eliminate the parameter ...Ch. 8.4 - The Rotary Engine The Mazda RX-8 uses an...Ch. 8.4 - Prob. 69ECh. 8.4 - DISCOVER WRITE: More Information in Parametric...Ch. 8.4 - Prob. 71ECh. 8 - (a) Explain the polar coordinate system. (b) Graph...Ch. 8 - Prob. 2RCCCh. 8 - Prob. 3RCCCh. 8 - Prob. 4RCCCh. 8 - Prob. 5RCCCh. 8 - Prob. 6RCCCh. 8 - Prob. 7RCCCh. 8 - Prob. 8RCCCh. 8 - Prob. 9RCCCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Rectangular Equations to Polar Equations (a)...Ch. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Polar Equations to Rectangular Equations (a)...Ch. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Finding Parametric Equations for a Curve In the...Ch. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - (a) Sketch the curve represented by the parametric...Ch. 8 - Find parametric equations for the line of slope 2...Ch. 8 - The position of an object in circular motion is...Ch. 8 - Prob. 1PCh. 8 - Path of a Baseball Suppose a baseball is thrown at...Ch. 8 - Path of a Rocket Suppose that a rocket is fired at...Ch. 8 - Firing a Missile The initial speed of a missile is...Ch. 8 - Prob. 5PCh. 8 - Shooting into the Wind Suppose that a projectile...Ch. 8 - Prob. 7P
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- Trajectories Are Parabolas From the graphs in Figure 3 the paths of projectiles appear to be parabolas that open downward. Eliminate the parameter r from the general parametric equations to verify that these are indeed parabolas. Figure (3) Paths of projectilesarrow_forwardEpicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.arrow_forwardShooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.arrow_forward
- Finding Parametric Equations for a Curve Two circles of radius a and b are centered at the origin, as shown in the figure. a Find parametric equations for the curve traced out by the point P, using the angle as the parameter. Note that the line segment AB is always tangent to the larger circle. b Graph the curve using a graphing device, with a=3 and b=2.arrow_forwardParametric equation x = (80 cos 45°)t, y = 6 + (80 sin 45°)t - 16t2; t = 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
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