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 in standard position, meaning it starts from the positive x-axis and rotates counterclockwise. Recall that one full rotation around the circle is $$2\pi$$ radians, so $$\frac{7\pi}{4} is $$less than $$2\pi$$ but more than $$\frac{3\pi}{2}$$, meaning the angle lies between $$270^\circ$$ and $$360^\circ in $$degree terms, but we keep it in radians as instructed. Note that $$\frac{7\pi}{4}$$ radians corresponds to $$2\pi - \frac{\pi}{4}$$, which means the angle is $$\frac{\pi}{4}$$ radians less than a full rotation, placing it in the fourth quadrant. To draw the angle, start at the positive x-axis (0 radians), then rotate counterclockwise around the circle until you reach $$\frac{7\pi}{4}$$ radians, which is three-quarters of the way around plus an additional $$\frac{\pi}{4}$$ radians. Mark the terminal side of the angle on the circle in the fourth quadrant, between the positive x-axis and the negative y-axis, and state that the angle lies in the fourth quadrant.

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 the Unit Circle

Quadrants of 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 the Unit Circle

Quadrants of 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