CONCEPT PREVIEW The terminal side of an angle θ in standard position passes through the point (― 3,― I3) Use the figure to find the following values. Rationalize denominators when applicable. r

Key Concepts

Standard Position of an Angle

In trigonometry, an angle is said to be in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The terminal side of the angle is determined by rotating the initial side counterclockwise. Understanding this concept is crucial for visualizing angles and their corresponding coordinates in the Cartesian plane.

Distance Formula

The distance formula is used to calculate the distance 'r' from the origin to a point (x, y) in the Cartesian plane. It is given by r = √(x² + y²). This formula is essential for finding the radius in polar coordinates and is often used in trigonometric problems to relate angles to their corresponding coordinates.

Rationalizing Denominators

Rationalizing the denominator is a mathematical process used to eliminate any radical expressions from the denominator of a fraction. This is often done by multiplying the numerator and denominator by a suitable value that will simplify the expression. In trigonometry, this technique is important for presenting answers in a standard form, especially when dealing with trigonometric ratios.