Trigonometry
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Determine the coordinates of the point on the plane curve represented by the following parametric equations for the specified value of u.
x = 7 − 9u, y = 6 + 4u; u = 3
x = (90 cos 60°)u, y = 12 + (90 sin 60°)u − 25u2; u = 4
Draw a graph of the plane curve defined by the following parametric equations with the help of point plotting. Indicate the direction of the curve obtained corresponding to increasing values of t using arrows.
x = t − 5, y = 3t + 2; −1 ≤ t ≤ 4
x = 5t, y = |t − 2|; -∞ < t < ∞
Write the corresponding rectangular equation for the following parametric equation by eliminating t. Draw a graph of the plane curve using the rectangular equation. Indicate the direction of the curve obtained corresponding to increasing values of t using arrows.
x = 3t, y = 7t; −∞ < t < ∞
x = √(2t), y = t - 3; −∞ < t < ∞
x = 4 + 7 cos t, y = 6 + 11 sin t; 0 ≤ t < 2π
x = 3t, y = 3-t; t ≥ 0
x = 11 - 6u, y = 8 + 3u; u = 5
x = u3 + 3, y = 7 − u4; u = 4
x = u5 + 3, y = 6 - u7; u = 1
x = 7 + 4 cos u, y = 8 + 11 sin u; u = π/2
Obtain two distinct sets of parametric equations corresponding to the following equation.
y = 9x - 5
y = x2 + 8
x = 11 + 7 cos u, y = 13 + 5 sin u; u = π
Plot the plane curve defined by the given set of parametric equations. Also, provide domain and range.
x = t2 +2t +11 and y = t
Write the corresponding rectangular equation for the following parametric equation by eliminating t. Draw a graph of the plane curve using the rectangular equation. Indicate the direction of the curve using arrows.
x = 5√t , y = t + 13; −∞ < t < ∞
Plot the plane curve defined by the given set of parametric equations.
x = t +1 and y = t3 -9
x = 5t +1, y = 7 − t; −∞ < t < ∞
x = 1 + 7cos t, y = 5 +7sin t; 0 ≤ t < 2π
x2 +777