1.4.1: Resources and Key Concepts — Read

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Resources

Unit Circle: The circle with a radius of 1 that is centered at the origin of the Cartesian plane. Its equation is \(x^2 + y^2 = 1\).
Quadrants: The four regions into which the Cartesian coordinate system is divided by the x- and y-axes. They are numbered I, II, III, and IV, starting from the top right and moving counterclockwise.
Standard Position of an Angle: An angle is in standard position if its vertex is located at the origin and its initial side lies along the positive x-axis.
Quadrantal Angle: An angle in standard position whose terminal side lies on either the x-axis or the y-axis.
Coterminal Angles: Angles that are in standard position and share the same terminal side.

Distance Formula: The distance \(d\) between two points \(P_1(x_1, y_1)\) and \(P_2(x_2, y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Equation of a Circle Centered at the Origin: The equation for a circle with radius \(r\) centered at the origin is \(x^2 + y^2 = r^2\).
Equation of a Circle Centered Off-Origin: The standard form for the equation of a circle with radius \(r\) centered at the point \((h, k)\) is \((x - h)^2 + (y - k)^2 = r^2\).
Coterminal Angle Formula: All angles that are coterminal with an angle \(\alpha\) can be expressed in the form \(\alpha + 360^\circ k\), where \(k\) is any integer.

Distributing a Radical over a Sum: A square root cannot be distributed across terms that are added or subtracted. For example, \(\sqrt{a^2 + b^2}\) is not equal to \(a + b\), and \(\sqrt{4 + 16}\) is not equal to \(\sqrt{4} + \sqrt{16}\). This is a critical mistake when using the Distance Formula.
Direction of Rotation for Angles: Positive angles are generated by a counterclockwise rotation from the initial side. Negative angles are generated by a clockwise rotation.

This page titled 1.4.1: Resources and Key Concepts was last modified on Sun, 31 Aug 2025 20:52:01 GMT and is shared under a CC BY-SA license and was authored, remixed, and/or curated by Roy Simpson.