Question

The tangent to the curve given by x = e^t . cost, y = e^t . sint at t = `pi/4` makes with x-axis an angle ______.

Options

• 0

• `pi/4`

• `pi/3`

• `pi/2`

Answer 1

The tangent to the curve given by x = e^t . cost, y = e^t . sint at t = `pi/4` makes with x-axis an angle `pi/2`.

Explanation:

`"dx"/"dt"` = – e^t . sint + e^tcost

`"dy"/"dt" = e^tcost + e^tsint

Therefore, `("dy"/"dx")_("t" = pi/4) = (cos"t" + sin"t")/(cos"t" - sin"t") = sqrt(2)/0`