Question

x=sec t, y=tan t, 0 t< π/ 2. A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

Answer 1

To sketch the curve represented by the given parametric equations x = sec(t) and y = tan(t), we need to find the corresponding values of x and y for different values of t. By choosing multiple values of t in the given range and finding the values of x and y, we can plot these points on a graph to sketch the curve.

Step-by-step explanation:

The given pair of parametric equations are:

x = sec(t)

y = tan(t)

To sketch the curve represented by these parametric equations, we need to find the values of x and y for different values of t. Since the given range is 0 < t < π/2, we can choose multiple values of t in this range and find the corresponding values of x and y.

Here are a few examples:

For t = 0, x = sec(0) = 1 and y = tan(0) = 0

For t = π/6, x = sec(π/6) = 2 and y = tan(π/6) = √3

For t = π/4, x = sec(π/4) = √2 and y = tan(π/4) = 1

We can continue finding values of x and y for different values of t and plot these points on a graph to sketch the curve represented by the parametric equations.