MHB Equation for tangent of the curve

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To find the equation of the tangent to the curve defined by the parametric equations x = 2 cos t and y = 2 sin t at t = π/3, the tangent line can be expressed as y - 2 sin(π/3) = m[x - 2 cos(π/3)], where m is the slope of the tangent line. The curve represents a circle with a radius of 2 centered at the origin. The slope m can be calculated using the derivative formula dy/dx = (dy/dt) / (dx/dt) evaluated at t = π/3. This approach provides a method to determine the slope of the tangent line at the specified point on the circle. Understanding these calculations is essential for accurately finding the tangent line's equation.
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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??
 
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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 $t=\dfrac{\pi}{3}$
 
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