1 degree =

Question

1 degree =

Examoogle · Accepted Answer

The correct answer is Option D: Both A and C. The relationship between degrees and radians is derived from the full circle geometry, where $360^{\circ} = 2\pi$ radians. Therefore, $1^{\circ} = \frac{2\pi}{360} = \frac{\pi}{180}$ radians, which numerically equals approximately 0.017453 radians, commonly rounded to 0.0175 radians.

Step-by-Step Solution & Concepts:
The relationship between degrees and radians is derived from the full circle geometry, where $360^{\circ} = 2\pi$ radians. Therefore, $1^{\circ} = \frac{2\pi}{360} = \frac{\pi}{180}$ radians, which numerically equals approximately 0.017453 radians, commonly rounded to 0.0175 radians.

Working Principle: In coordinate geometry and structural mechanics, angular rotation is often required in radians for consistency in calculus-based deflection formulas. Since the arc length $s$ equals the radius $r$ times the angle $	heta$ in radians ($s = r	heta$), converting degrees to radians is a fundamental prerequisite for slope calculations in beam analysis.

Key Formulas: $	ext{Radians} = 	ext{Degrees} 	imes \frac{\pi}{180}$ — Conversion formula; $	heta_{rad} = \frac{s}{r}$ — Definition of angle in radians

Key Points: A radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.; Calculations for slope and deflection in Structural Mechanics almost exclusively use radians to maintain compatibility with trigonometric series expansions like $\sin(	heta) \approx 	heta$.; The factor $\frac{\pi}{180}$ is the standard conversion multiplier used in engineering software and scientific calculators.

Advantages: Radians simplify derivative and integral operations in calculus.; Eliminates the need for empirical correction factors in structural formulas.

Disadvantages: Degree notation is more intuitive for human spatial visualization in site work.; Requires conversion steps for inputs from traditional survey instruments.

Applications: Structural slope and deflection analysis; Computer-Aided Design (CAD) software algorithms; Torsional rigidity and rotation calculations

Additional Info: 1 radian is approximately 57.296 degrees.. Option B (2\pi/180) is equal to \pi/90, which is 2 degrees, hence mathematically incorrect.

Answer: D is correct — Since $1^{\circ} = \frac{\pi}{180}$ radians and $\frac{\pi}{180} \approx 0.017453$ radians, both A and C are correct representations of the value.

Exam Tip: Always ensure your calculator is in 'RAD' mode when solving structural deflection problems involving slopes or rotations; 'DEG' mode will result in significant errors.

Examoogle · Answer

Option A: $0.0175 	ext{ radian}$

Examoogle · Answer

Option B: $\frac{2\pi}{180} 	ext{ radian}$

Examoogle · Answer

Option C: $\frac{\pi}{180} 	ext{ radian}$

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