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

The ordered pair is:
`((7√(3))/(2),(5√(3))/(2))`

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 = (\pi)/(6)`

`x = 7 \cos{(\pi)/(6)} = 7(√(3))/(2) = (7√(3))/(2)`

`y = 5 \cos{(\pi)/(6)} = 5(√(3))/(2) = (5√(3))/(2)`

The ordered pair is:
`((7√(3))/(2),(5√(3))/(2))`