Question

1. # Find The Slope Of The Tangent Line To The Polar Curve R=2−Sin(Θ) At The Point Specified By Θ=Π/3.

Calculus is a complex subject, and one of its most difficult concepts to understand is finding the slope of a tangent line to a polar curve. This article will explain how you can use polar coordinates to find the slope of the tangent line to the polar curve r=2−sin(θ) at the point specified by θ=π/3. We will also provide an example that demonstrates how you can use derivatives effectively to solve this problem. By the end of this article, you should have a better understanding of how to find the slope of the tangent line to any polar equation at any given point.

## What is the Slope of the Tangent Line?

To find the slope of the tangent line to the curve at a given point, we need to take the derivative of the function at that point. In this case, we are taking the derivative of −sin(Θ). The derivative of −sin(Θ) is −cos(Θ). Therefore, the slope of the tangent line to the curve at Θ=Π/ is −cos(Π/).

## How to Find the Slope of the Tangent Line

There are a few different ways that you can find the slope of the tangent line to the polar curve R=-Sin(Θ) at the point specified by Θ=Π/:

1. You can use the definition of the derivative to find the slope.

2. You can use the formula for the derivative of a parametric curve.

3. You can use calculus to find the slope of the tangent line.

## The Slope of the Tangent Line at the Point Specified by Θ=Π/3

At the point where θ=Π/3, the slope of the tangent line to the curve R=-sin(Θ) is -1/√3. This can be seen by taking the derivative of R with respect to Θ, which gives us -cos(Θ). At θ=Π/3, cos(Θ)=-1/2, so the slope of the tangent line at this point is -1/(2*√3)=-1/√3.

## Conclusion

In this article we have discussed how to find the slope of a tangent line to a polar curve at the specified point Θ = π/3. We first examined how to convert from polar coordinates, then evaluated the derivative of R=2-sin(Θ) and found that it had a value of -1 at Θ = π/3. Finally, we determined that the slope of the tangent line is m=-1. With an understanding of these concepts, you can now easily calculate any similar problems involving derivatives in polar coordinates.

2. Have you ever wondered how to calculate the slope of the tangent line to a polar curve at a given point?

If so, then you’ve come to the right place! Today, we’ll be finding the slope of the tangent line to the polar curve R = 2 – sin(Θ) at the point specified by Θ = π/3.

To begin, we’ll need to use the formula for the derivative of a polar equation. The derivative of a polar equation is the first derivative of the equation, with respect to the angle Θ. This means that we can calculate the slope of the tangent line at a given point by finding the derivative of the equation at that point.

To find the derivative of the equation, we must first rewrite it as a function of Θ. This can be done by solving for R:

R = 2 – sin(Θ)

R – 2 = – sin(Θ)

R + sin(Θ) = 2

We can now take the derivative of this equation:

d/dΘ (R + sin(Θ)) = d/dΘ (2)

d/dΘ (R + sin(Θ)) = 0

d/dΘ (R) + d/dΘ (sin(Θ)) = 0

1 + cos(Θ) = 0

cos(Θ) = -1

Now that we have the derivative, we can calculate the slope of the tangent line at the given point. To do this, we must substitute in Θ = π/3:

cos(π/3) = -1

Slope of the tangent line = -1

Therefore, the slope of the tangent line to the polar curve R = 2 – sin(Θ) at the point specified by Θ = π/3 is -1.