Question

For the plane curve defined by x = 7 cos t, y = 5 cos t, for t in [0, 2π​] the ordered pair that corresponds to t = π/6 is ___

Answer 1

Answer:

The ordered pair is: $(\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})$

Step-by-step explanation:

We are given the following plane curve:

$x = 7 \cos{t}$

$y = 5 \cos{t}$

Ordered pair for a value of t:

We find (x,y) for these values of t. So, when $t = \frac{\pi}{6}$

$x = 7 \cos{\frac{\pi}{6}} = 7\frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}$

$y = 5 \cos{\frac{\pi}{6}} = 5\frac{\sqrt{3}}{2} = \frac{5\sqrt{3}}{2}$

The ordered pair is: $(\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})$