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Question
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle ______.
Options
0
`pi/4`
`pi/3`
`pi/2`
Solution
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle `pi/2`.
Explanation:
`"dx"/"dt"` = – et . sint + etcost
`"dy"/"dt" = etcost + etsint
Therefore, `("dy"/"dx")_("t" = pi/4) = (cos"t" + sin"t")/(cos"t" - sin"t") = sqrt(2)/0`
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