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15=4π rad/s×r×sin⁡(15∘)15 = 4\pi \text{ rad/s} \times r \times \sin(15^\circ)

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Full solution

Q. 15=4π rad/s×r×sin⁡(15∘)15 = 4\pi \text{ rad/s} \times r \times \sin(15^\circ)
  1. Understand and Isolate Variable: Understand the equation and isolate the variable rr. The equation given is 15=4π rad/s×r×sin⁡(15∘)15 = 4\pi \, \text{rad/s} \times r \times \sin(15^\circ). We need to solve for rr, which means we need to isolate rr on one side of the equation. To do this, we will divide both sides of the equation by 4π rad/s×sin⁡(15∘)4\pi \, \text{rad/s} \times \sin(15^\circ).
  2. Divide by Constant: Divide both sides of the equation by 4π rad/s×sin⁡(15∘)4\pi \, \text{rad/s} \times \sin(15^\circ). \newliner=154π rad/s×sin⁡(15∘)r = \frac{15}{4\pi \, \text{rad/s} \times \sin(15^\circ)}
  3. Calculate sin⁡(15∘)\sin(15^\circ): Calculate sin⁡(15∘)\sin(15^\circ).\newlinesin⁡(15∘)\sin(15^\circ) is a trigonometric function value that can be found using a calculator or trigonometric tables. For the sake of this problem, we will use a calculator.\newlinesin⁡(15∘)≈0.2588\sin(15^\circ) \approx 0.2588 (rounded to four decimal places)
  4. Substitute and Solve for r: Substitute sin⁡(15°)\sin(15°) into the equation and solve for rr.r=15(4π×0.2588)r = \frac{15}{(4\pi \times 0.2588)}
  5. Perform Calculation: Perform the calculation.\newliner≈15(4×π×0.2588)r \approx \frac{15}{(4 \times \pi \times 0.2588)}\newliner≈15(3.1416×1.0352)r \approx \frac{15}{(3.1416 \times 1.0352)}\newliner≈153.2527r \approx \frac{15}{3.2527}\newliner≈4.6112r \approx 4.6112 (rounded to four decimal places)

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