Answer
(a) The percent uncertainty in $\theta$ is 3%.
The percent uncertainty in $sin(\theta)$ is 3%.
(b) The percent uncertainty in $\theta$ is 0.7%.
The percent uncertainty in $sin(\theta)$ is 0.2%.
Work Step by Step
(a) $\frac{0.5^{\circ}}{15^{\circ}}\times 100\% = 3\%$
$\frac{sin(15.0^{\circ} - sin(14.5^{\circ}))}{sin(15.0^{\circ})}\times 100\% = 3\%$
The percent uncertainty in $\theta$ is 3%.
The percent uncertainty in $sin(\theta)$ is 3%.
(b) $\frac{0.5^{\circ}}{75^{\circ}}\times 100\% = 0.7\%$
$\frac{sin(75.0^{\circ} - sin(74.5^{\circ}))}{sin(75.0^{\circ})}\times 100\% = 0.2\%$
The percent uncertainty in $\theta$ is 0.7%.
The percent uncertainty in $sin(\theta)$ is 0.2%.
