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

Question

Quizplus · Accepted Answer

For small angles, we can use the approximation sin θ ≈ θ (in radians).
So, sin θ = sin(10°) ≈ 0.1745 and θ in radians = 10° × π/180 ≈ 0.1745.
The percent difference can be found using the formula: (|sin θ - θ|/((sin θ + θ)/2)) × 100%
Plugging in the values, we get:
(|0.1745 - 0.1745|/((0.1745 + 0.1745)/2)) × 100% = 0%
Therefore, the percent difference between sin θ and θ in radians is 0%, which is closest to option C: 0.5%.

For an Angle of 10 Degrees, What Is the Percent