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Scelta multipla
Identify the quadrant that the given angle is located in. 7π radians
A
Quadrant I
B
Quadrant II
C
Quadrant III
D
Quadrant IV
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1
Convert the given angle \( \frac{\pi}{7} \) radians into degrees for easier interpretation, if necessary. Use the conversion formula \( \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \).
Understand that a full circle is \( 2\pi \) radians (or 360 degrees), and each quadrant represents a quarter of the circle: Quadrant I (0 to \( \frac{\pi}{2} \)), Quadrant II (\( \frac{\pi}{2} \) to \( \pi \)), Quadrant III (\( \pi \) to \( \frac{3\pi}{2} \)), and Quadrant IV (\( \frac{3\pi}{2} \) to \( 2\pi \)).
Compare \( \frac{\pi}{7} \) to the boundaries of the quadrants. Since \( \frac{\pi}{7} \) is a small positive angle, it lies between 0 and \( \frac{\pi}{2} \), which corresponds to Quadrant I.
Verify your conclusion by considering the unit circle. In Quadrant I, both the sine and cosine of the angle are positive, which aligns with the properties of \( \frac{\pi}{7} \).
Conclude that the angle \( \frac{\pi}{7} \) radians is located in Quadrant I.