Questions: Which of the following images shows an angle of -285° in standard position?

Transcript text: Which of the following images shows an angle of $-285^{\circ}$ in standard position?

Solution

Solution Steps

To determine which image shows an angle of $-285^{\circ}$ in standard position, we need to convert the negative angle to a positive angle by adding $360^{\circ}$ until the angle is within the range of $0^{\circ}$ to $360^{\circ}$. Then, we can identify the corresponding position on the unit circle.

Step 1: Convert the Negative Angle to a Positive Angle

To find the equivalent positive angle of $-285^\circ$, we add $360^\circ$ until the angle is within the range of $0^\circ$ to $360^\circ$.

\[ -285^\circ + 360^\circ = 75^\circ \]

Step 2: Identify the Position on the Unit Circle

The angle $75^\circ$ is in the first quadrant of the unit circle. This is because $75^\circ$ is between $0^\circ$ and $90^\circ$.