A student measured an angle θ = 41 ± 1°. convert the value to radians. calculate sin (θ). evaluate the uncertainty in the measured value of the sin θ. note that the uncertainty in θ, δθ is not equal to the uncertainty in sin θ, δsin θ. one simple way of determining the uncertainty in sin θ is by δsin θ = (sin θmax - sin θmin) / 2, where θmax = θ + δθ and θmin = θ - δθ. remember, that any uncertainty calculation is just an estimate, so don't report more than two significant digits!

Question

Ryan Patel

Mathematics

4 September, 22:17

A student measured an angle θ = 41 ± 1°. convert the value to radians. calculate sin (θ). evaluate the uncertainty in the measured value of the sin θ. note that the uncertainty in θ, δθ is not equal to the uncertainty in sin θ, δsin θ. one simple way of determining the uncertainty in sin θ is by δsin θ = (sin θmax - sin θmin) / 2, where θmax = θ + δθ and θmin = θ - δθ. remember, that any uncertainty calculation is just an estimate, so don't report more than two significant digits!

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Alexis Morgan · Answer 1

Angle = 41 degrees

Conversion to radians:

41° = 41*π/180 = 0.7156 radians

1° = 1*π/180 = 0.0175

Angle measured in radians = 0.7156+/-0.0175

Sin (angle):

Sin (0.7156) = 0.6561

Uncertainty in Sin (0.7156) = (Sin∅ max - Sin∅ min) / 2 = (Sin 0.7330 - Sin 0.6981) / 2 = 0.0132

Sin ∅ = 0.06561+/-0.0132