Trigonometry and Polar Coordinates Practice Test

A rescue helicopter is located at polar coordinates $(r,\theta)=(24,,210^\circ)$ relative to a base, where $r$ is kilometers. The base uses rectangular coordinates with $x$ positive east and $y$ positive north. The angle is given in degrees and measured counterclockwise from the positive $x$-axis. Convert using exact trigonometric values, not decimals. Convert the polar coordinates to rectangular coordinates $(x,y)$ for the helicopter.​

A rotating beacon’s intensity model uses the expression $I(\theta)=\sin\theta\cos\theta$, where $\theta$ is measured in radians. A technician rewrites the model using a single trigonometric function to simplify computations. Use exactly one standard identity and do not approximate. The angle variable remains in radians throughout. Using the identity, simplify the expression for $I(\theta)$.​