7. Use a calculator to determine \( \theta \) to the nearest degree. \( \begin{array}{lll}\text { a) } \cos \theta=0.6820 & \text { b) } \tan \theta=0.1944 & \text { c) } \sin \theta=0.9848\end{array} \)

To find \( \theta \) in each case, you would use the inverse trigonometric functions on your calculator. For \( \cos \theta = 0.6820 \), you would input \(\cos^{-1}(0.6820)\) which approximately gives you \( \theta \approx 47^\circ\). For \( \tan \theta = 0.1944\), you would use \(\tan^{-1}(0.1944)\), resulting in \( \theta \approx 11^\circ\). Lastly, \( \sin \theta = 0.9848\) would lead you to \( \theta \approx 80^\circ\) with \(\sin^{-1}(0.9848)\). Always remember to ensure your calculator is set to the correct mode: degrees versus radians! A common mistake is forgetting to switch this, which can lead to overly confusing results when solving trig problems. Also, keep in mind that angles can have multiple values depending on the context or quadrant, so be sure to assess what range your \( \theta \) should fall into!