THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Small-angle approximations
Estimate an approximation’s error
A calculation replaces sin θ by θ at θ = 0.12 rad. Use sin θ ≈ θ − θ³/6.
Estimate (θ − sin θ)/θ to leading order.
Organize the givens & assumptions
- θ = 0.12 rad
- Use sin θ ≈ θ − θ³/6
- Fractional difference is defined relative to θ
Small positive angle in radians. The denominator is explicitly θ; keep only the stated leading correction.
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