MHB Equation for tangent of the curve

[juliehellowell]

Can anyone help me to find the equation of the tangent to the curve x = 2 cos t, y= 2 sin t where t= pi/3??

 

[skeeter]

The set of parametric equations define a circle of radius, $r=2$, centered at the origin.

Tangent line to this circle has equation

$y - 2\sin\left(\dfrac{\pi}{3}\right) = m\bigg[x - 2\cos\left(\dfrac{\pi}{3}\right) \bigg]$

where $m$ is the slope perpendicular to the radius that connects the center to the point $(x,y)$ on the circle at $t=\dfrac{\pi}{3}$

you may also determine the slope, $m$, if you know how to calculate $\dfrac{dy}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}$ at $t=\dfrac{\pi}{3}$