A physical quantity is defined as S = x * cos(theta), where x = (2.0 +/- 0.2) cm and theta = (53 +/- 2) degrees. Calculate S along with its absolute error.

1.2 +/- 0.18 cm
1.2 +/- 0.15 cm
1.2 +/- 0.23 cm
1.2 +/- 0.27 cm

Correct answer: 1.2 +/- 0.18 cm

Solution

S = 2.0 * cos(53 deg) = 2.0 * 0.6 = 1.2 cm. The absolute error DeltaS = S*(Deltax/x + tan(theta)*Dtheta_rad) = 1.2*(0.1 + 1.327*0.03491) = 1.2*0.1463 = 0.1756 approx 0.18 cm.

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