A curve is represented parametrically by the equations `x = e^t cos t and y = e^t sin t` where t is a parameter. Then The relation between the parameter 't' and the angle a between the tangent to the given curve andthe x-axis is given by, 't' equals

Options

A. `(pi)/2-alpha=t`
B. `(pi)/4+alpha=t`
C. `(pi)/4-alpha=t`
D. `alpha-(pi)/4=t`

Answer

D

Explanation

`y=e^(t)sintimplies(dy)/(dx) =e^(t)[cost+sint]`
`x=e^(t)costimplies(dx)/(dt)=e^(t)[cost-sint]`
`:.(dy)/(dx)=(cost+sint)/(cost-sint)=tanalpha`
`:.tan((pi)/4+t)=tanalpha`
`((pi)/4+t)=alpha`
`t=alpha-(pi)/4`