Questions: Find a positive angle and a negative angle that is coterminal to -5π/4. □ is a positive angle that is coterminal to -5π/4. □ is a negative angle that is coterminal to -5π/4. π

Solution Steps

To find coterminal angles, we add or subtract multiples of \(2\pi\) to the given angle. For a positive coterminal angle, add \(2\pi\) until the result is positive. For a negative coterminal angle, subtract \(2\pi\) until the result is negative.

To find a positive angle coterminal with \( -\frac{5\pi}{4} \), we add \( 2\pi \) until the result is positive. The calculation yields: \[ \text{Positive Coterminal Angle} = -\frac{5\pi}{4} + 2\pi = 2.3562 \quad (\text{rounded to four significant digits}) \]

To find a negative angle coterminal with \( -\frac{5\pi}{4} \), we subtract \( 2\pi \) until the result is negative. The calculation yields: \[ \text{Negative Coterminal Angle} = -\frac{5\pi}{4} - 2\pi = -10.2102 \quad (\text{rounded to four significant digits}) \]

Final Answer