# Equation for tangent of the curve

• MHB
• juliehellowell
In summary, the set of parametric equations x = 2 cos t, y = 2 sin t where t = pi/3 define a circle of radius 2 centered at the origin. The equation of the tangent line to this circle at t = pi/3 is y - 2sin(pi/3) = m(x - 2cos(pi/3)), where m is the slope perpendicular to the radius connecting the center to the point on the circle. The slope, m, can be determined by calculating dy/dx at t = pi/3 using the formula dy/dx = (dy/dt)/(dx/dt).
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??

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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## 1. What is the equation for tangent of a curve?

The equation for tangent of a curve is y = tan(x), where x is the angle of inclination and y is the slope of the tangent line at that point on the curve.

## 2. How is the equation for tangent of a curve derived?

The equation for tangent of a curve is derived from the formula for slope, which is rise over run. In other words, the tangent line at a point on a curve represents the slope of the curve at that point.

## 3. What does the equation for tangent of a curve tell us?

The equation for tangent of a curve tells us the slope of the curve at any given point. This can be useful in determining the rate of change or the direction of the curve at a specific point.

## 4. Can the equation for tangent of a curve be used to find the equation of the tangent line?

Yes, the equation for tangent of a curve can be used to find the equation of the tangent line at a specific point on the curve. This can be done by plugging in the x-coordinate of the point into the equation and solving for y.

## 5. Is the equation for tangent of a curve the same for all types of curves?

No, the equation for tangent of a curve may differ depending on the type of curve. For example, the equation for tangent of a circle would be different from the equation for tangent of a parabola. However, the concept of slope and the use of the tangent line to determine the slope at a point remains the same.

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