For the following exercises, find the reference angle, the...

For the following exercises, find the reference angle, the quadrant of the terminal side, and the sine and cosine of each angle. If the angle is not one of the angles on the unit circle, use a calculator and round to three decimal places.
$$
\frac{4 \pi}{3}
$$

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Key Concepts

Reference Angle

The reference angle is the acute angle, always less than 90° (or ?/2 radians), that the terminal side of an angle makes with the nearest horizontal axis. It is used to determine the magnitude of trigonometric function values by considering the symmetry of the unit circle.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, and the quadrant in which an angle’s terminal side lies determines the sign of its sine and cosine values. Recognizing the quadrant helps in understanding the behavior of trigonometric functions for different angles.

Sine and Cosine Functions

Sine and cosine are fundamental trigonometric functions that, on the unit circle, represent the y- and x-coordinates of a point on the circle, respectively. Their values are computed based on the angle’s position and are essential in linking geometric and algebraic representations of angles.

Unit Circle

The unit circle is a circle of radius one centered at the origin, which provides a geometric framework for defining trigonometric functions in terms of angles measured in radians. It is a central concept in trigonometry, allowing for the visual interpretation of sine, cosine, and related functions.

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