Meriam, Kraige & Bolton — Introduction to Statics: Problem 1_11

⚡ Mecademy AIENG정역학 · ch1  Problem Statement 1/11 Evaluate the expression for . Then use the small- angle assumptions and repeat the calculation. Problem 1/11 (a) Exact Evaluation ● Calculation Process 1. Present Final Formula: First, we can simplify the expression using the trigonometric identity . 2. Substitute Values: Substitute into the simplified expression. 3. Partial Operations: Calculate the sine of and then its cube. 4. Final Calculation: Multiply by 3. ● Final Conclusion: The exact value of the expression is approximately: (b) Evaluation using Small-Angle Assumptions ● Calculation Process 1. Present Final Formula: For a small angle (expressed in radians), the following approximations hold: E=3sinθtanθcosθ 2 θ=2 ∘ tanθ= cosθ sinθ E=3sinθtanθcosθ= 2 3sin θ cos θ = 2 ( cosθ sinθ )3sinθ 3 θ=2 ∘ E=3sin(2) 3∘ 2 ∘ sin(2)≈ ∘ 0.0348995 sin(2)≈ 3∘ (0.0348995)≈ 3 0.0000425095 E=3×0.0000425095≈0.000127528 E=1.275×10 −4 θ Applying these to the original expression : 2. Substitute Values: First, convert the angle from degrees to radians. Substitute this into the approximate formula: 3. Partial Operations: Calculate the value of the angle in radians and its cube. 4. Final Calculation: Multiply by 3. ● Final Conclusion: Using the small-angle assumptions, the value of the expression is approximately: ✨ Final Answer Summary (a) Exact value: (b) Small-angle approximation value: Mecademy AI Solution · ENGProblem 1/11 sinθ≈θ,tanθ≈θ,cosθ≈1 E=3sinθtanθcosθ 2 E≈3(θ)(θ)(1)= 2 3θ 3 θ=2 ∘ θ =