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.

14𝜋/3

Accepted Answer

Identify that the angle given is $$\frac{14\pi}{3}$$ radians, which is greater than $$2\pi$$ radians (one full rotation around the circle). To find the equivalent angle within one full rotation, subtract multiples of $$2\pi$$ from $$\frac{14\pi}{3}$$ until the result is between $$0$$ and $$2\pi. $$Use the formula: $$	heta_{equiv} = 	heta - 2\pi 	imes k$$, where $$k is an $$integer. Calculate $$k by $$dividing the numerator of the angle by the denominator times 2 (i.e., $$k = \left\lfloor \frac{14}{3 	imes 2} ightfloor$$), then subtract $$2\pi k$$ from $$\frac{14\pi}{3} to $$get the equivalent angle in radians. Once you have the equivalent angle, determine its position on the unit circle by comparing it to the standard quadrant boundaries: 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 ($$\frac{3\pi}{2} to$$ $$2\pi). $$Draw the angle in standard position starting from the positive x-axis and moving counterclockwise by the equivalent angle measure. State the quadrant where the terminal side of the angle lies.

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.

14𝜋/3

Verified video answer for a similar problem:

Key Concepts

Angles in Standard Position

Radian Measure and Circle Rotation

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.14𝜋/3

Verified video answer for a similar problem:

Key Concepts

Angles in Standard Position

Radian Measure and Circle Rotation

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.

14𝜋/3