Question
\begin{tabular}{l} In which quadrant does the terminal side of a \( \frac{\pi}{4} \) radian angle in standard position lie? \\ Quadrant I \\ Quadrant II \\ \hline Quadrant IV \\ \hline\end{tabular}
Ask by Reese Luna. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The terminal side of a \( \frac{\pi}{4} \) radian angle is in Quadrant I.
Solution
The terminal side of a π/4 radian angle is in Quadrant I.
Explanation:
An angle of π/4 radians is equivalent to 45°. When an angle in standard position has a measure of 45° (less than 90°), it lies in the first quadrant.
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Simplify this solution Mind Expander
The terminal side of a \( \frac{\pi}{4} \) radian angle, which is equivalent to 45 degrees, lies in Quadrant I. In this quadrant, both the x-coordinates and y-coordinates are positive, making it a lively and vibrant part of the coordinate plane! If you’re ever confused about angles, remember that angles measured in radians can be converted to degrees using the conversion factor \( \frac{180}{\pi} \). This means that \( \frac{\pi}{4} \) is just a quarter of a full rotation, landing you right in the first quadrant where all the positive vibes and helpful trig functions like sine and cosine (both equal to \( \frac{\sqrt{2}}{2} \)) thrive!
