Select the Parametric Equations Matching with the Following Graph $x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )$

question 47

Multiple Choice

Select the parametric equations matching with the following graph.

• A) Involute of circle: \(x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )\)
• B) Involute of circle: \(x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \cos \theta )\)
• C) Involute of circle: \(x = \frac { 1 } { 3 } ( \cos \theta - \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \theta \cos \theta )\)
• D) Involute of circle: \(x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta + \theta \cos \theta )\)
• E) Involute of circle: \(x = \frac { 1 } { 3 } ( \cos \theta + \theta \sin \theta ) , y = \frac { 1 } { 3 } ( \sin \theta - \cos \theta )\)

---

Definitions:

Insurance Companies

Businesses that provide coverage, in the form of compensation resulting from loss, damages, injury, treatment or hardship in exchange for premium payments.

Lifetime Annuity

An insurance product that provides the holder with guaranteed income for the rest of their life.

Adverse Selection

A situation in finance and insurance where parties with higher risk are more likely to engage in agreements, potentially leading to imbalances in the market.

Actuarial Error

Mistakes in the calculations or assumptions made by actuaries, which can affect insurance premiums, pension plans, and other financial assessments.