47–48 - Graphs of Parametric Equations Use a graphing device to draw the parametric curve. 47. x = cos 21, y= sin 31 48. x = sin(1 + cos 21), y = cos(t + sin 31)
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- 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.A pair of parametric equations is given. sin?(t), y = sin*(t) X = (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases.PARAMETRIC EQUATIONS. Find the second derivative of y with respect to x from the parametric equations given. 4) x=√1-t₁y = t³ - 3t 5) x 1 1/t, y = 6-7/t + 2/t² -
- Parametric 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.Parametric equation x = 2 + 3 cos t, y = 4 + 2 sin t; t = π 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.The path of a projectile that is launched h feet above the ground with an initial velocity of vo feet per second and at an angle 0 with the horizontal is given by the parametric equations shown below, where t is the time, in seconds, after the projectile was launched. x= (vo cos 0) t, y=h+ (Vo sin 0) t-16t2 Use a graphing utility to obtain the path of a projectile launched from the ground (h=0) at an angle of 0 = 65° and initial velocity of v = 130 feet per second. Use the graph to determine the maximum height of the projectile and the time at which it reaches this height, as well as the range of the projectile and the time it hits the ground. Choose the correct graph of the path of the projectile. OA. Q G OB. ○ C. O D. Q Q E G [0,1000]x[0,300] [0,1000] x [0,300] [0,1000]x[0,300] What is the maximum height of the projectile? feet (Type an integer or decimal rounded to the nearest tenth as needed.) At what time does the projectile reach this maximum height? seconds (Type an integer or…
- Use a graphing utility to graph each set of parametric equations. x = t − sin t, y = 1 − cos t, 0 ≤ t ≤ 2π x = 2t − sin(2t), y = 1 − cos(2t), 0 ≤ t ≤ π (a) Compare the graphs of the two sets of parametric equations in earlier part. When the curve represents the motion of a particle and t is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?Use 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 THANKSParametric equation x = t2 + 1, y = 5 - t3; 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.
- 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 32. (parametric curves) Find a parametric equation for the following curve using 0 as the parameter and (0, 0) as the terminal point: 0 y = √x (x, y)The trajectory of a projectile launched from the origin at an initial speed of u at an angle of 0 degrees to the horizontal is given by the parametric equations x = v cos(0)t y=- 1 I 9t² where g is acceleration due to gravity, typically 32 feet per second per second or 9.8 meters per second per second. +vsin (0)t Find parametric equations for the trajectory of a golf ball with an initial speed of 80 feet per second at an angle of 60° to the horizontal. Enter either exact value coefficients (in radians!!!) or correct to at least three decimal places. Y 80 cos 60 7 ) 180 t sin (60 180) . How many seconds will the ball be -16² +80 sin 60- the air before it hits the ground? seconds How far will it travel horizontally in total? feet