Question

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

7𝜋/4

Accepted Answer

Identify that the angle given is $$\frac{7\pi}{4}$$ radians, which is measured in standard position starting from the positive x-axis and moving counterclockwise. Recall that one full revolution around the circle is $$2\pi$$ radians, so $$\frac{7\pi}{4} is $$less than $$2\pi$$ and lies within one full rotation. Note that the circle is divided into four quadrants, each spanning $$\frac{\pi}{2}$$ radians: Quadrant I from $$0 to$$ $$\frac{\pi}{2}$$, Quadrant II from $$\frac{\pi}{2} to$$ $$\pi$$, Quadrant III from $$\pi to$$ $$\frac{3\pi}{2}$$, and Quadrant IV from $$\frac{3\pi}{2} to$$ $$2\pi. $$Since $$\frac{7\pi}{4} is $$between $$\frac{3\pi}{2}$$ and $$2\pi$$, the terminal side of the angle lies in Quadrant IV. To draw the angle, start at the positive x-axis and rotate counterclockwise through $$\frac{7\pi}{4}$$ radians, which corresponds to 3 full $$\frac{\pi}{2}$$ quadrants plus an additional $$\frac{\pi}{4}$$, ending in Quadrant IV.

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

7𝜋/4

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angles in Standard Position

Radian Measure and Circle Division

Quadrants in the Coordinate Plane

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.7𝜋/4

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angles in Standard Position

Radian Measure and Circle Division

Quadrants in the Coordinate Plane

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

7𝜋/4