Question

The small angle approximation is often made to simplify derivations and calculations. For the following angles θ, compare the true value of the sine of the angle to the to the small angle approximation (using only the first term in the series expansion of the sine) by determining the fractional error (let the fractional error be positive). NOTE: If you explicitly use π to convert from degrees to radians, use an accurate value for it.

DIGRESSION: The fractional error is the difference between the approximate or measured value and the "known or true" value divided by the known or true value.

a) θ = 1.04°:
Fractional Error = ______
b) θ = 4.65°:
Fractional Error = ______
c) θ = 16.70°:
Fractional Error = ______
d) θ = 40.97°:
Fractional Error = ______

We are keeping the values of the period with 5 significant figures (or 4th decimal place). Look at the results above and select angles which will give an error much larger (in physics it normally means x10 and higher) than the measurement limit assumed in this lab.

Is it A B C or D? (You may choose more than one as your answer)

Answer 1

(by small angle approximation)

(a) (true )

(approx)

Fractional error = 5.4*10^-5

(b)(true)

(approx)

Fractional error = 0.00109

(c)(true)

(approx)

Fractional error = 0.014300

(d) (true)

(approx)

Fractional error = 0.090592

Checking the values , greater the angle , greater is the fractional error.