Equation of the Tangent Line and Area of Parametric Equation I need to find the equation of the tangent line to the point (1,0) for the equation:

$x=e^{-0.1t}cos(t) \\
y=e^{-0.1t}sin(t)$

I also need to calculate the area in the first quadrant bounded on the outside by the curve for $t$ greater than or equal to $0$ and less than or equal to $\pi/2$.

I am not totally sure what to do for either one.

I know that $\frac{dy}{dx}$ is $\frac{dy}{dt}/\frac{dx}{dt}$. 

Is the tangent line equation $y=\frac{dy}{dx}(x-1)$?  Once I calculate $\frac{dy}{dx}$ I'd just plug it in to the equation.
Hint:

For the first part, you can find the (unnormalized) tangent vector $T(t)$ at the point $p(t) = (1,0)$ on the curve by calculating the derivative with respect to the parameter, $t$: $$T(t) = \frac{dx}{dt}\hat{i} + \frac{dy}{dt}\hat{j}$$

For the second part, find the polar form of the curve $r = f(\theta)$. Then the area is $$\iint f(\theta) \ r \ dr \ d\theta$$ You'll also need to figure out the appropriate limits of integration.
Hint:

For the first part, you can find the (unnormalized) tangent vector $T(t)$ at the point $p(t) = (1,0)$ on the curve by calculating the derivative with respect to the parameter, $t$: $$T(t) = \frac{dx}{dt}\hat{i} + \frac{dy}{dt}\hat{j}$$

For the second part, find the polar form of the curve $r = f(\theta)$. Then the area is $$\iint f(\theta) \ r \ dr \ d\theta$$ You'll also need to figure out the appropriate limits of integration.