Question

For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 5%?

Answer 1

31°

Explanation:

Comparing θ and sin(θ) really only makes sense when both are expressed in radians. A graphing calculator shows θ/sin(θ) = 1.05 for θ ≈ 0.538 radians. That angle value is approximately 30.8 degrees.

θ ≈ 31° when the error in sin(θ) ≈ θ is 5%.

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Check

31° ≈ 0.541 radians

sin(31°) ≈ 0.515

The difference between these values is about 5.05% of sin(31°).