The page you’ve shared appears to contain calculations related to physics, particularly involving rotational motion or trigonometric analysis.

Here’s a breakdown of what I can interpret from the image:

1. Velocity Calculation: $\text{tan } \theta = \frac{\pi (0.07)(60)}{60}$ This expression simplifies, resulting in: $\approx 0.21 \, \text{m/s}$ This part seems to calculate a velocity or speed.

2. Angle Calculation: $\cos \alpha_1 = \frac{r_1 - r_2}{x}$ Plugging in values: $\cos \alpha_1 = \frac{0.035 - 0.02}{0.14} = 0.107$ This gives: $\alpha_1 = \cos^{-1}(0.107) \approx 82.86^\circ \approx 1.44 \, \text{radians}$

3. Further Angle Calculation: $\theta_2 = 2 \alpha_1$ Substituting: $\theta_2 = 2 \times 1.44 \approx 2.88 \, \text{radians}$

Let me know if you’d like any further details on each step or if there’s a specific part of this solution you need help with.

Related Questions:

1. What is the significance of using radians vs. degrees in angular calculations?
2. How does the choice of values (e.g., $r_1, r_2, x$) impact the final angle?
3. What scenarios would require calculating angles using cosine versus other trigonometric functions?
4. How would the solution differ if another constant were introduced?
5. Can you explain the role of the tangent function in calculating velocities?

Tip: When calculating angles, remember to check if your calculator is set to degrees or radians, as this affects the outcome directly.