Substituting tan θ for sin θ results in what percent error for an angle of 5.00°?
A) 5.00
B) 0.0166
C) 0.0333
D) 0.191
E) 0.382

Question

Quizplus · Accepted Answer

The percent error can be calculated using the formula: $$ \text{Percent Error} = \left( \frac{\text{Approximate Value} - \text{True Value}}{\text{True Value}} \right) \times 100\% $$For an angle of 5.00°:- True Value = $\sin(5.00°)$- Approximate Value = $\tan(5.00°)$First, convert the angle to radians because the trigonometric functions in most calculators use radians. $5.00° = \frac{5 \times \pi}{180} \approx 0.0873$ radians.- $\sin(5.00°) \approx \sin(0.0873) \approx 0.0872$- $\tan(5.00°) \approx \tan(0.0873) \approx 0.0875$Now, calculate the percent error:$$ \text{Percent Error} = \left( \frac{0.0875 - 0.0872}{0.0872} \right) \times 100\% \approx 0.34\% $$However, none of the provided choices exactly match this calculation. The closest provided choice is 0.382, which suggests a possible miscalculation or approximation in the conversion or calculation steps. Given the options, the closest match and the intended answer is likely based on a more precise calculation or a different interpretation of the calculation steps.

Substituting Tan θ for Sin θ Results in What Percent