# Which is orientation of tangential angle in polar coordinates?

• Jhenrique
In cartesian coordinates, φ is the angle that the tangent to the curve makes with the positive direction of the x-axis. Therefore, the tangential angle depends on the coordinate system being used. In summary, the tangential angle is the angle that the tangent to a curve makes with a reference axis, and its orientation varies based on the coordinate system being used.
Jhenrique
In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the orientation these angles aren't specified. In cartesian coordinates, I believe that the tangential angle φ is measured from the x-axis, in polar coordinates the tangential angle ψ is measured from radial axis?

https://en.wikipedia.org/wiki/Subtangent
https://en.wikipedia.org/wiki/Tangential_angle

Jhenrique said:
In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the orientation these angles aren't specified. In cartesian coordinates, I believe that the tangential angle φ is measured from the x-axis, in polar coordinates the tangential angle ψ is measured from radial axis?

https://en.wikipedia.org/wiki/Subtangent
https://en.wikipedia.org/wiki/Tangential_angle
From your reference, it looks like, in polar coordinates, ψ is the angle that the tangent to the curve makes with a unit vector in the radial direction at the specified point.

## 1. What is the definition of tangential angle in polar coordinates?

The tangential angle in polar coordinates is the angle between the positive x-axis and the tangent line drawn from the origin to a point on the polar curve. It is measured in a counterclockwise direction.

## 2. How is the tangential angle calculated in polar coordinates?

The tangential angle can be calculated using the formula atan(dy/dx), where dy/dx is the derivative of the polar curve at the desired point. Alternatively, it can also be calculated using the formula atan(y/x), where x and y are the coordinates of the point on the polar curve.

## 3. What is the range of values for the tangential angle in polar coordinates?

The tangential angle can have values between 0 and 360 degrees, or between 0 and 2π radians. This is because the polar coordinate system is a circular system, so the angles wrap around after reaching 360 degrees or 2π radians.

## 4. How does the orientation of the tangential angle affect the direction of motion in polar coordinates?

The orientation of the tangential angle determines the direction of motion at a specific point on the polar curve. If the tangential angle is positive, the motion is counterclockwise, and if it is negative, the motion is clockwise. A tangential angle of 0 degrees or 0 radians indicates no motion.

## 5. Can the tangential angle in polar coordinates be negative?

Yes, the tangential angle in polar coordinates can be negative. As mentioned before, a negative tangential angle indicates a clockwise motion along the polar curve.

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