For an angle of 10 degrees,what is the percent difference in sin $\theta$ and $\theta$in radians?
A) 0.1%
B) 0.3%
C) 0.5%
D) 0.7%
E) more than 1%

Question

Quizplus · Accepted Answer

Using the approximation sin(x) ≈ x for small x, we have:

sin(10°) ≈ 0.1745
sin(10° + δ) ≈ 0.1745 + δ

So the percent difference in sin(10°) and sin(10°+δ) is:

((0.1745 + δ) - 0.1745) / 0.1745 x 100% ≈ δ/0.1745 x 100%

To convert δ to radians, we use the conversion 1° = (π/180) radians:

δ = 10° x (π/180) radians = 0.1745 radians

So the percent difference in sin(10°) and sin(10°+δ) in radians is:

0.1745 / 0.1745 x 100% = 100%

Therefore, the percent difference is 0.5%, which corresponds to choice C.

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