Angle between Radius Vector & Tangent - Part 1 | Derivation | Engineering Mathematics

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Angle between Radius Vector & Tangent
Part 1 - • Angle between Radius V...
Part 2 - • Angle between Radius V...
The concept of the angle between the radius vector and tangent is an important topic in engineering mathematics, particularly in the study of polar curves. In Engineering Mathematics 1, students learn about the relationship between the radius vector and tangent vector of a curve, and how this relationship can be used to find the angle of intersection between two curves.
The radius vector is a vector that connects the origin to a point on a curve, while the tangent vector is a vector that is perpendicular to the radius vector at that same point. The angle between these two vectors is known as the angle between the radius vector and tangent, and it is measured in radians.
To find the angle between the radius vector and tangent to a curve, one can use the formula: θ = tan⁻¹(dy/dx), where dy/dx is the derivative of the polar equation with respect to theta.
In practical applications, engineers often use polar curves to model various physical phenomena, such as the motion of a projectile or the shape of a satellite orbit. Examples of polar curves include Archimedes spiral, cardioid, and limaçon.
When dealing with the intersection of two polar curves, it is important to find the angle of intersection, which is the angle between the two tangent vectors at the point of intersection. This angle can be found using the dot product of the two tangent vectors, which gives the cosine of the angle between them.
Overall, the angle between the radius vector and tangent is an important concept in engineering mathematics that has numerous practical applications in a variety of fields.
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0:01 - Example #1 - tan phi=r(d theta)/(d gamma) or cot phi=(1)/(r)(d gamma)/(d theta)
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