In Exercises 8–12, draw each angle in standard position. 5𝜋 6

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Understand that an angle in standard position is drawn with its vertex at the origin of the coordinate plane, its initial side along the positive x-axis, and the angle measured counterclockwise for positive angles.

Identify the given angle: \(\frac{5\pi}{6}\). This is a radian measure, so recall that \(\pi\) radians equals 180 degrees.

Convert the angle to degrees if it helps visualization: multiply by \(\frac{180}{\pi}\) to get \(\frac{5\pi}{6} \times \frac{180}{\pi} = 150^\circ\).

Draw the initial side along the positive x-axis. From there, measure an angle of 150 degrees counterclockwise to locate the terminal side of the angle.

Mark the terminal side of the angle in the second quadrant, since 150 degrees is between 90 and 180 degrees, and label the angle as \(\frac{5\pi}{6}\) radians.

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주요 개념

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Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of the coordinate plane, its initial side lies along the positive x-axis, and the angle is measured by rotating the initial side to the terminal side. Understanding this helps in accurately drawing and interpreting angles.

Radian Measure

Radian measure expresses angles based on the radius of a circle, where 2π radians equal 360 degrees. Knowing how to convert and interpret radians, such as 5π/6, is essential for drawing angles and solving trigonometric problems.

Unit Circle and Reference Angles

The unit circle is a circle with radius 1 centered at the origin, used to define trigonometric functions. Reference angles help determine the position of an angle's terminal side by relating it to a known acute angle, facilitating accurate drawing and analysis.