Mathematics

Mathematics

Problem

A teacher states that the small-angle approximation is appropriate if sin⁡θ\sin\theta differs from θ\theta by less than 5%5\%. A student pulls a pendulum to an initial angle of 20∘20^{\circ} before release. Which of the following is most nearly correct about using the small-angle approximation for this release angle? a) The difference between sin⁡θ\sin\theta and θ\theta is about 0.7%0.7\%, so the approximation is acceptable. b) The difference between sin⁡θ\sin\theta and θ\theta is about 6%6\%, so the approximation is not acceptable. c) The difference between sin⁡θ\sin\theta and θ\theta is about 2%2\%, so the approximation is acceptable. d) The difference between sin⁡θ\sin\theta and θ\theta is about 4%4\%, so the approximation is acceptable.

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